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AMDOCS Probability Problems with Solutions Quiz-1

Question 1

Time: 00:00:00

A bag contains 4 white, 5 red and 6 blue balls. Three balls are drawn at random from the bag. The
probability that all of them are red, is:

43122

43181

2/91

2/77

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Probability of 1st ball = red is 5/(4+5+6) = 5/15.

P(2nd ball = red) = 4/14 as only 4 red balls remain if 1st ball = red. Out of 14.

P(3rd ball = red) is 3/13.

Answer = 5/15 * 4/14 * 3/13
= 2/91

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Question 2

Time: 00:00:00

A box contains 20 electric bulbs, out of which 4 are defective. Two bulbs are chosen at random
from this box. The probability that at least one of these is defective, is:

43209

1/5

5/6

21/95

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Total bulbs = 20
Defective = 4
Non - defective = 20-4 =16

Probability that at least one of these is defective = 4/20
= 1/5

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Question 3

Time: 00:00:00

In a class, 30% of the students offered English, 20% offered Hindi and 10% offered both. If a
student is selected at random, what is the probability that he has offered English or Hindi ?

3/10

2/5

5/6

6/8

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30/100

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Question 4

Time: 00:00:00

A box contains 6 red balls, 7 green balls and 5 blue balls. Each ball is of a different size. The
probability that the red ball being selected is the smallest red ball, is

1/18

2/5

6/9

5/7

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Question 5

Time: 00:00:00

If A and B are 2 independent events and P(A)=0.5 and P(B) = 0.4, find P(A/B):

1.8

0.4

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p(a/b)=p(a+b)/p(b)

=0.9/0.5

=1.8

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Question 6

Time: 00:00:00

A company needs to choose a team of 4 from a group of 3 content managers, 3 R&D engineers and 5 client engagement managers for the completion of a project. What is the probability that exactly 3 of them are client engagement managers?

2/11

23/87

231

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Total members = 3+3+5 = 11
Total no. of ways of selection 4 members is 11C4 = 330
No. of ways of selecting exactly 3 client eng managers are
3 from client (AND) 1 from content managers
(OR)
3 from client (AND) 1 from R&D
=> 5C3*3C1 + 5C3*3C1 = 30 + 30 = 60
Prob. ll be 60/330 = 2/11

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Question 7

Time: 00:00:00

A manufacturing company produces a batch of 10 containers out of which 4 are defective. In a quality inspection, 3 containers are chosen at random. What is the probability that at least one is defective?

5/6

4/8

2/3

43/87

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5/6

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Question 8

Time: 00:00:00

A biased die has a probability of 1/4 of showing a 5, while the probability of any of 1, 2, 3, 4, or 6 turning up is the same . If three such dice are rolled, what is the probability of getting a sum of atleast 14 without getting a 6 on any die ?

7/160

43102

43254

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Probability of getting 5 = 1/4
Probability of getting 1,2,3,4 or 6 = 1 – 1/4 = 3/4
Therefore
probability of getting 1 = (3/4)/5 = 3/20
probability of getting 2 = (3/4)/5 = 3/20
probability of getting 3 = (3/4)/5 = 3/20
probability of getting 4 = (3/4)/5 = 3/20
probability of getting 6 = (3/4)/5 = 3/20
Event: 3 dice rolled and their sum should be atleast 14 without getting a 6 on any dice.
ie (5,5,5) , (4,5,5),(5,4,5),(5,5,4)
Probability of getting (5,5,5) = 1/4*1/4*1/4 = 1/64
Probability of getting (4,5,5) = 3/20*1/4*1/4 = 3/320
Probability of getting (5,4,5) = 1/4*3/20*1/4 = 3/320
Probability of getting (5,5,4) = 1/4*1/4*3/20 = 3/320
Probability of getting a sum of atlest 14
= 1/64 + 3/320 + 3/320 + 3/320
= 7/160

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Question 9

Time: 00:00:00

What is the probability of getting the sum 5 in two
throws of the dice?

43112

1/5

43109

43134

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1/5

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Question 10

Time: 00:00:00

Seema cannot completely remember her four-digit ATM pin number. She does remember the first two digits, and she knows that each of the last two digits is greater than 5. The ATM will allow her three tries before it blocks further access. If she randomly guesses the last two digits, what is the probability that she will get access to her account?

43102

3/16

43/65

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Explanation:

no of cases for the last two digits are

66 76 86 96

67 77 87 97

68 78 88 98

69 79 89 99

so there are total 16 cases and no of chances are only 3 so probability of getting access will be 3/16.

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["0","40","60","80","100"]

["Need more practice! \r\n","Keep trying! \r\n","Not bad! \r\n","Good work! \r\n","Perfect! \r\n"]

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