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GMAT Probability Questions

Here is a set of 14 GMAT probability questions, all in the Problem Solving style on the test, collected from a series of blog articles.  Answers and links to explanations to these these GMAT probability problems are at the end of set.

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The scenario below is relevant to questions #1-#3.

There are two sets of letters, and you are going to pick exactly one letter from each set.

Set #1 = {A, B, C, D, E}

Set #2 = {K, L, M, N, O, P}

1) What is the probability of picking a C and an M?

    (A) 1/30
    (B) 1/15
    (C) 1/6
    (D) 1/5
    (E) 1/3

2) What is the probability of picking a C or an M?

    (A) 1/30
    (B) 1/15
    (C) 1/6
    (D) 1/5
    (E) 1/3

3) What is the probability of picking two vowels?

    (A) 1/30
    (B) 1/15
    (C) 1/6
    (D) 1/5
    (E) 1/3

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4) In a certain corporation, there are 300 male employees and 100 female employees.  It is known that 20% of the male employees have advanced degrees and 40% of the females have advanced degrees.  If one of the 400 employees is chosen at random, what is the probability this employee has an advanced degree and is female?

    (A) 1/20
    (B) 1/10
    (C) 1/5
    (D) 2/5
    (E) 3/4

5) In a certain corporation, there are 300 male employees and 100 female employees.  It is known that 20% of the male employees have advanced degrees and 40% of the females have advanced degrees.  If one of the 400 employees is chosen at random, what is the probability this employee has an advanced degree or is female?

    (A) 1/20
    (B) 1/10
    (C) 1/5
    (D) 2/5
    (E) 3/4

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Set #1 = {A, B, C, D, E}

Set #2 = {K, L, M, N, O, P}

6) There are these two sets of letters, and you are going to pick exactly one letter from each set.  What is the probability of picking at least one vowel?

    (A) 1/6
    (B) 1/3
    (C) 1/2
    (D) 2/3
    (E) 5/6

7) Suppose you flip a fair coin six times.  What is the probability that, in six flips, you get at least one head?

    (A) 5/8
    (B) 13/16
    (C) 15/16
    (D) 31/32
    (E) 63/64

8) In a certain game, you pick a card from a standard deck of 52 cards.  If the card is a heart, you win.  If the card is not a heart, the person replaces the card to the deck, reshuffles, and draws again.  The person keeps repeating that process until he picks a heart, and the point is to measure: how many draws did it take before the person picked a heart and won?   What is the probability that one will have at least three draws before one picks a heart?

    (A) 1/2
    (B) 9/16
    (C) 11/16
    (D) 13/16
    (E) 15/16

9) Five children, AnaxagorasBeatriceChildericDesdemona, and Ethelred, sit randomly in five chairs in a row.   What is the probability that Childeric and Ethelred sit next to each other?

    (A) 1/30
    (B) 1/15
    (C) 1/5
    (D) 2/5
    (E) 7/20

10) A division of a company consists of seven men and five women.  If two of these twelve employees are randomly selected as representatives of the division, what is the probability that both representatives will be female?

    (A) 1/6
    (B) 2/5
    (C) 2/9
    (D) 5/12
    (E) 5/33

11) John has on his shelf four books of poetry, four novels, and two reference works.  Suppose from these ten books, we were to pick two books at random.  What is the probability that we pick one novel and one reference work?

    (A) 1/2
    (B) 2/5
    (C) 3/10
    (D) 7/20
    (E) 8/45

gpq_img1

12) In the diagram above, the sides of rectangle ABCD have a ratio AB:BC = 1:2, and the circle is tangent to three sides of the rectangle.  If a point is chosen at random inside the rectangle, what is the probability that it is not inside the circle?

gpq_img2

13) Region R is a square in the x-y plane with vertices J = (–1, –2), K = (–1, 4), L = (5, 4), and M = (5, –2).  What is the probability that a randomly selected point in region R lies below the line 3x – 5y = 10?

    (A) 5/12
    (B) 5/18
    (C) 5/24
    (D) 5/36
    (E) 5/72

gpq_img3

14) In the diagram above, WZ = XZ, and circular arc XY has a center at W.  If a point is selected from anywhere within this figure, what is the probability that it is selected from the shaded region?

gpq_img4

Summary

If you have comments or questions, please let us know in the comment section at the bottom! 🙂

 

Answers

1) A

2) E

3) B

4) B

5) D

6) C

7) E

8) B

9) D

10) E

11) E

12) D

13) C

14) A

 

Explanations

For the explanations for #1-5, see this post.

For the explanations for #6-8, see this post.

For the explanations for #9-11, see this post.

For the explanations for #12-14, see this post.

Check out this post if you want a wider range of Problem Solving sample questions.

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16 Responses to GMAT Probability Questions

  1. Kevin March 27, 2017 at 12:33 am #

    Hello, question on #2,
    I wanted to be creative by applying the following logic (assuming that it should come down to the same probability).

    What is the probability of picking a C and then a non-M (1/5 x 5/6) = 1/6
    What is the probability of picking a non C and then an M (4/5 x 1/6) = 4/30 = 2/15

    If I add the above two probability, I would expect to get the same result (3/10) as picking C or M, but I am getting 9/30 instead of 10/30.

    Please, can you see where my logic fails?

    Thank you,

    • Magoosh Test Prep Expert
      Magoosh Test Prep Expert March 27, 2017 at 6:42 am #

      Hi Kevin,

      Great question! You’re actually almost there. So, the question ask: “What is the probability of picking a C or an M?”. You’ve captured is the first probability only getting a “C”, and in the second probability only getting a “M”. You have to also calculate picking a C and M. The question asks for the probability of picking a C or an M, but does not say to only one of those.

      So, you have:

      = “9/30” + “probability of picking both C and M”
      = 9/30 + (1/5)(1/6)
      = 9/30 + 1/30
      = 10/30
      = 1/3

      I hope this helps! 😀

  2. Maria October 14, 2016 at 3:04 pm #

    I really appreciate your help!!

    I am wondering what the answer to the following question would be:

    “Tom has 32 ties, 5 are blue, 16 are yellow and 11 are red. What is the probability of picking one which is either red or yellow?”

    I thought it may be :
    numerator: disjoint events: 11/32+16/32
    denominator: 32!

    is this correct?
    many many tnanks!!

    • Magoosh Test Prep Expert
      Magoosh Test Prep Expert October 14, 2016 at 4:03 pm #

      Hi Maria,

      Based on how the question is phrased, you may actually be overanalyzing the problem. It sounds like you have 32 ties (5 blue; 16 yellow; 11 red), and you’re going to pick one tie out. The question is asking what is the probability that this one tie will be red or yellow. So, it is simply:

      Probability of Red/Yellow Tie = (Red Ties + Yellow Ties) / (Total Ties) = (11 + 16) / 32 = 27 / 32. You have a “27/32” probability that you will pick a red or yellow tie.

  3. Brian Freeman August 23, 2016 at 11:36 pm #

    Hey Mike,

    Can you explain why the answer to #6 is C and not B? Here’s my logic:

    P(at least 1 vowel) = 1 – P(no vowels)
    P(at least 1 vowel) = 1 – (4/5)*(5/6)
    P(at least 1 vowel) = 1 – (20/30) = (10/30) = (1/3)

    • Magoosh Test Prep Expert
      Magoosh Test Prep Expert August 27, 2016 at 7:54 pm #

      Hi Brian,

      Your reasoning and methods are right, but you said that P(no vowels) for the first set was 4/5, when in fact it is 3/5 (there are two vowels: A and E). When you change this an multiply your fractions out, you will get the correct answer of 1/2. You can also see a more in-depth explanation to this question in this blog post: http://magoosh.com/gmat/2012/gmat-math-the-probability-at-least-question/ 🙂

  4. Ujjwal June 25, 2015 at 6:07 am #

    Hello Mike

    Can you please explain answer question number 8 . I could not figure out the “at least” scenario. We have not be given the number of try picker has to perform. so in simple words we can not apply the complementary rule as defined in the approach .

    Now the question is as follows :-

    “the person keeps repeating that process until he picks a heart, and the point is to measure: how many draws did it take before the person picked a heart and won? What is the probability that one will have at least three draws before one picks a heart?”

    So he has to pick at least three times and we are not given the number of tries ,so lets imagine that he picked total of 4 times and in the 4th time he won ! so now the probability is p(getting heart)=1-p(not getting a heart once)

    1-(3/4)(3/4)(3/4)= 47/64 .

    request you to please explain the answer .

    Thanks and regards
    Ujjwal

  5. K July 25, 2014 at 10:53 am #

    Hi Mike,

    Can you please explain why Answer 2 is not 1/5+1/6=11/30? Instead you say it is 1/3?

    (Ref: What is the probability of picking a C or an M?)

    Thanks
    K

    • Mike MᶜGarry
      Mike July 25, 2014 at 1:22 pm #

      Dear K,
      I’m happy to respond. 🙂 It’s very important not to confuse ordinary OR with exclusive OR — in computer science, the latter is sometimes denoted XOR. Ordinary OR includes the overlap case — “C or M” includes (1) C only, (2) M only, and (3) both C and M. Exclusive OR, XOR, would include the first two but not the third. Whenever you see “OR” given in a GMAT question, with no further restrictions or stipulations, you have to assume that it is an ordinary OR and never an exclusive OR.
      In addition, I would say: you need to learn about the generalized OR rule. See this post:
      http://magoosh.com/gmat/2012/gmat-math-probability-rules/
      Mike 🙂

      • Srishti Sinha August 21, 2015 at 12:25 am #

        Wow! Now I know my mistake.. Thanks for the explanation.

        Regards,
        Srish

  6. Leszek June 15, 2014 at 11:25 am #

    How come in question 11 the answer is not 4/45?
    My logic is as follows:
    1) the probability of choosing one novel out of 10 books = 4/10 times
    2) the probability of choosing one reference work out of 9 books = 2/9

    4/10*2/9=8/90 or 4/45

    Best

    • Mike MᶜGarry
      Mike June 15, 2014 at 12:38 pm #

      Dear Leszek,
      I’m happy to respond. 🙂 This is one of the tricky things about probability: it’s sometimes hard to see what assumptions the calculations implies. By saying novel = 4/10, then reference = 2/9, then you are implicitly assuming that the novel is picked first, and the reference work is picked second. To get the result of a novel + reference work, it doesn’t matter which one was picked first, and this means we would have to calculate both orders and add them, which gives us the answer of 8/45.
      Does this make sense?
      Mike 🙂

      • Leszek June 15, 2014 at 1:14 pm #

        Sure – makes a lot of sense!

        thanks

        • Mike MᶜGarry
          Mike June 16, 2014 at 10:14 am #

          Dear Leszek,
          You are quite welcome. Best of luck to you, my friend.
          Mike 🙂

  7. Meera September 29, 2013 at 12:43 am #

    I think the #9 option D is 2/5 and not 2/15.

    • Mike MᶜGarry
      Mike September 29, 2013 at 10:31 am #

      Meera,
      Yes! You are perfectly correct. It should be 2/5 — I just made that correction. Thank you very much for pointing that out.
      Mike 🙂


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