some probability questions,good for practice

[skawal]

1.There are 9 beads in a bag. 3 beads are red, 3 beads are blue, and 3 beads are black. If two beads are chosen at random, what is the probability that they are both blue?

 

A. 1/81

 

B. 1/12

 

C. 2/9

 

D. 1/3

 

E. 1/4

 

2 A letter is randomly selected from the word Mississippi. What is the probability that the letter will be an s?

 

A. 1/11

 

B. 3/10

 

C. 4/11

 

D. 1/4

 

E. 1/3

 

3. A certain deck of cards contains 2 blue cards, 2 red cards, 2 yellow cards, and 2 green cards. If two cards are randomly drawn from the deck, what is the probability that they will both are not blue?

 

A. 15/28

 

B. 1/4

 

C. 9/16

 

D. 1/32

 

E. 1/16

 

4. A fair coin is tossed, and a fair six-sided die is rolled. What is the probability that the coin come up heads and the die will come up 1 or 2?

 

A. 1/2

 

B. 1/4

 

C. 1/6

 

D. 1/12

 

E. 1/3

 

5. A bag of 10 marbles contains 3 red marbles and 7 blue marbles. If two marbles are selected at random, what is the probability that at least one marble is blue?

 

A. 21/50

 

B. 3/13

 

C. 47/50

 

D. 14/15

 

E. 1/5

 

6. A fair, six-sided die is rolled. What is the probability that the number will be odd?

 

A. 1/4

 

B. 1/2

 

C. 1/3

 

D. 1/6

 

E. 1/5

 

7. A letter is randomly select from the word studious. What is the probability that the letter be a U?

 

A. 1/8

 

B. 1/4

 

C. 1/3

 

D. 1/2

 

E. 3/8

 

8. A bag contains 2 red beads, 2 blue beads, and 2 green beads. Sara randomly draws a bead from the bag, and then Victor randomly draws a bead from the bag. What is the probability that Sara will draw a red marble and Victor will draw a blue marble?

 

A. 2/13

 

B. 1/5

 

C. 1/3

 

D. 1/10

 

E. 2/15

 

9. If two fair, six-sided dice are rolled, what is the probability that the sum of the numbers will be 5?

 

A. 1/6

 

B. 1/4

 

C. 1/36

 

D. 1/18

 

E. 1/9

 

10. If four fair coins are tossed, what is the probability of all four coming up heads?

 

A. 1/4

 

B. 1/6

 

C. 1/8

 

D. 1/16

 

E. 1/32

 

11. The probability that a certain event will occur is 5/9. What is the probability that the event will NOT occur?

 

A. 5/9

 

B. 4/9

 

C. 2/9

 

D. 1/4

 

E. 1/2

 

12. A certain bag contains red, blue, yellow, and green marbles. If a marble is randomly drawn from the bag, the probability of drawing a blue marble is .2, the probability of drawing a red marble is .3, and the probability of drawing a yellow marble is .1. What is the probability of drawing a green marble?

 

A. .5

 

B. .6

 

C. .2

 

D. .4

 

E. .3

 

13. A bag contains 3 red marbles, 3 blue marbles, and 3 green marbles. If a marble is randomly drawn from the bag and a fair, six-sided die is tossed, what is the probability of obtaining a red marble and a 6?

 

A. 1/15

 

B. 1/6

 

C. 1/3

 

D. 1/4

 

E. 1/18

 

14. A fair, six-sided die is rolled. What is the probability of obtaining a 3 or an odd number?

 

A. 1/6

 

B. 1/5

 

C. 1/4

 

D. 2/3

 

E. 1/2

 

15. At a certain business school, 400 students are members of the sailing club, the wine club, or both. If 200 students are members of the wine club and 50 students are members of both clubs, what is the probability that a student chosen at random is a member of the sailing club?

 

A. 1/2

 

B. 5/8

 

C. 1/4

 

D. 3/8

 

E. 3/5

 

16. A bag contains six marbles: two red, two blue, and two green. If two marbles are drawn at random, what is the probability that they are the same color?

 

A. 1/3

 

B. 1/2

 

C. 1/8

 

D. 1/4

 

E. 1/5

 

17. There are five students in a study group: two finance majors and three accounting majors. If two students are chosen at random, what is the probability that they are both accounting students?

 

A. 3/10

 

B. 2/5

 

C. 1/5

 

D. 3/5

 

E. 4/5

 

18. Seven beads are in a bag: three blue, two red, and two green. If three beads are randomly drawn from the bag, what is the probability that they are not all blue?

 

A. 5/7

 

B. 23/24

 

C. 6/7

 

D. 34/35

 

E. 8/13

 

19. A bag has six red marbles and six blue marbles. If two marbles are drawn randomly from the bag, what is the probability that they will both be red?

 

A. 1/2

 

B. 11/12

 

C. 5/12

 

D. 5/22

 

E. 1/3:)

[v-rap]

Anybody tried solving these ?

[mickgreen58]

3) Why isn't the answer 1-1/28 = 27/28?

[skawal]

Dear mick,i coolect the problems from the gmat forrum.there they dont provide the OA.i think best solutions would be draw out by some healthy discussions.[clap]

[mickgreen58]

Dear mick,i coolect the problems from the gmat forrum.there they dont provide the OA.i think best solutions would be draw out by some healthy discussions.[clap]

 

I agree.

 

You have 8 total cards

 

2 of them are blue

 

They want to know what is the probability that when you choose 2 randomly, they won't be blue.

 

I would think the easiest way is to find out the probability of picking a blue card in a row which would be:

1/4*1/7 = 1/28

1 - 1/28 = probability that you won't get blue twice?

[hilldog]

1. B [ 3/9 * 2/8 = 1/12 ]

2. C [ 4/11 ]

3. ? [ 1-2/8 * 1/7 = 27/28]

4. C [ 1/2 * 2/6 = 1/6 ]

5. D [ 1-3/10*2/9 = 14/15 ]

6. B [ 3/6 = 1/2 ]

7. B [ 2/8 = 1/4 ]

8. E [ 2/6 * 2/5 = 2/15 ]

9. E [ 4/36 = 1/9 ]

10. D [ 1/2*1/2*1/2*1/2 = 1/16 ]

11. B [ 1-5/9 = 4/9 ]

12. D [ 1-0.2-0.3-0.1 = 0.4 ]

13. E [ 3/9*1/6 = 1/18 ]

14. E [ 3/6 = 1/2 ]

15. B

only wine=200-50=150

only sailing = 400-50-150=200

sailing=200+50=250

probability=250/400=5/8

16. E [ 3 * 2/6 * 1/5 = 1/5 ]

17. A [ 3/5 * 2/4 = 3/10 ]

18. D [ 1- 3/7 * 2/6 * 1/5 = 34/35 ]

19. D [ 6/12 * 5/11 = 5/22 ]

[Mervin2008]

Thanks for the problems ,anyone has any idea on how to do the third one,I am still confused about that.

[JonRiemann]

Question 3 is poorly written. It's asking for the probability that neither of the selected cards is blue.

 

3/4 * 5/7 = 15/28

 

A is the correct answer.

 

 

 

Note: This answer is obviously correct, but we can double-check this by using the somewhat more complicated method of finding the probability that at least one is blue and then substracting from 1.

 

Remember P(X) + P(Y) - P(X and Y)

 

That gives 1/4 + 1/4 - (1/4*1/7) = 13/28 is the probability that at least one is blue.

 

Thus, the probability of neither being blue is

 

1 - 13/28 = 15/28

 

This matches up with our earlier (and much easier to obtain) answer, so we know we're right.

[mickgreen58]

Question 3 is poorly written. It's asking for the probability that neither of the selected cards is blue.

 

3/4 * 5/7 = 15/28

 

A is the correct answer.

 

 

 

Note: This answer is obviously correct, but we can double-check this by using the somewhat more complicated method of finding the probability that at least one is blue and then substracting from 1.

 

Remember P(X) + P(Y) - P(X and Y)

 

That gives 1/4 + 1/4 - (1/4*1/7) = 13/28 is the probability that at least one is blue.

 

Thus, the probability of neither being blue is

 

1 - 13/28 = 15/28

 

This matches up with our earlier (and much easier to obtain) answer, so we know we're right.

 

How are you getting the 3/4 and 5/7?

[dimpylz]

For #3 can't you just say the probability of not getting blue twice would be 6/8*5/7 = 30/56=15/28???

 

Wouldn't it just be the opposite of getting a blue twice? You have a 6/8 chance of not getting a blue the first time, and if you don't get a blue again the second time, you have a 5/7 chance (because there is one less non-blue color the second time).

[mickgreen58]

For #3 can't you just say the probability of not getting blue twice would be 6/8*5/7 = 30/56=15/28???

 

Wouldn't it just be the opposite of getting a blue twice? You have a 6/8 chance of not getting a blue the first time, and if you don't get a blue again the second time, you have a 5/7 chance (because there is one less non-blue color the second time).

 

Hmm, that is a good way of looking at it.

 

I just thought you could find the P of not getting a blue ball in two tries would be: 1 - P(getting blue 1st time) + P(getting blue 2nd time)?

 

1 - 2/8 + 1/7?

[JonRiemann]

For #3 can't you just say the probability of not getting blue twice would be 6/8*5/7 = 30/56=15/28???

).

 

Exactly. 6/8 (or as I put, 3/4) * 5/7 will get you your answer.

 

Question 3 is not written in good English. I think that's why everyone is having such a hard time with it.

[shahadatme]

1. B [ 3/9 * 2/8 = 1/12 ]

2. C [ 4/11 ]

3. ? [ 1-2/8 * 1/7 = 27/28]

4. C [ 1/2 * 2/6 = 1/6 ]

5. D [ 1-3/10*2/9 = 14/15 ]

6. B [ 3/6 = 1/2 ]

7. B [ 2/8 = 1/4 ]

8. E [ 2/6 * 2/5 = 2/15 ]

9. E [ 4/36 = 1/9 ]

10. D [ 1/2*1/2*1/2*1/2 = 1/16 ]

11. B [ 1-5/9 = 4/9 ]

12. D [ 1-0.2-0.3-0.1 = 0.4 ]

13. E [ 3/9*1/6 = 1/18 ]

14. E [ 3/6 = 1/2 ]

15. B

only wine=200-50=150

only sailing = 400-50-150=200

sailing=200+50=250

probability=250/400=5/8

16. E [ 3 * 2/6 * 1/5 = 1/5 ]

17. A [ 3/5 * 2/4 = 3/10 ]

18. D [ 1- 3/7 * 2/6 * 1/5 = 34/35 ]

19. D [ 6/12 * 5/11 = 5/22 ]

 

Q14: I think the ans should be D. Because p=1/6+3/6

=4/6 =2/3

 

So the ans is D.:hmm:

[Dorlen4]

16. A bag contains six marbles: two red, two blue, and two green. If two marbles are drawn at random, what is the probability that they are the same color?

 

the answer is:

 

[ 3 * 2/6 * 1/5 = 1/5 ]

 

 

Can someone please clear up why 2/6 was multiplied by 3 in the answer? I know how we got 2/6 and 1/5 but im confused with the 3!!

 

Thanks !

[Goldust]

The 3 refers to the the 3 separate cases of red, blue and green pairs.