Statistics & Probability for Competitive Exam Success

Statistics & Probability

Bayes Theorem Conditional Probability Measures of Central Tendency Measures of Dispersion Probability Basics

Q. A die is rolled. What is the probability of getting an even number given that the number rolled is greater than 2?

A. 1/2
B. 1/3
C. 2/3
D. 1/4

Solution

The possible outcomes greater than 2 are {3, 4, 5, 6}. The even numbers among these are {4, 6}. Thus, the probability is 2/4 = 1/2.

Correct Answer: C — 2/3

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Q. A die is rolled. What is the probability of getting an even number?

A. 1/2
B. 1/3
C. 1/6
D. 2/3

Solution

Even numbers on a die: 2, 4, 6. Probability = 3/6 = 1/2.

Correct Answer: A — 1/2

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Q. A die is rolled. What is the probability of rolling an even number given that the number rolled is greater than 2?

A. 1/2
B. 1/3
C. 1/4
D. 2/3

Solution

The possible outcomes greater than 2 are {3, 4, 5, 6}. The even numbers among these are {4, 6}. Thus, the probability is 2/3.

Correct Answer: D — 2/3

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Q. A die is rolled. What is the probability of rolling an even number?

A. 1/2
B. 1/3
C. 1/6
D. 2/3

Solution

The even numbers on a die are 2, 4, and 6, which gives us 3 favorable outcomes. The total outcomes are 6. Therefore, the probability is 3/6 = 1/2.

Correct Answer: A — 1/2

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Q. A family has 2 children. What is the probability that both children are boys if it is known that at least one is a boy?

A. 1/2
B. 1/3
C. 1/4
D. 1/5

Solution

The possible combinations of children are BB, BG, GB, GG. Given that at least one is a boy, we can eliminate GG, leaving us with BB, BG, GB. Out of these 3 combinations, only 1 is BB. Therefore, the probability is 1/3.

Correct Answer: B — 1/3

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Q. A family has 2 children. What is the probability that both children are boys, given that at least one is a boy?

A. 1/3
B. 1/2
C. 1/4
D. 2/3

Solution

The possible combinations are BB, BG, GB. Given at least one is a boy, the combinations are BB, BG, GB. The probability of both being boys is 1/3.

Correct Answer: A — 1/3

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Q. A family has 2 children. What is the probability that both children are boys?

A. 1/4
B. 1/2
C. 1/3
D. 1/5

Solution

The possible combinations of children are BB, BG, GB, GG. Out of these, only 1 combination is both boys (BB). Thus, the probability is 1/4.

Correct Answer: A — 1/4

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Q. A family has 3 children. What is the probability that at least one child is a girl given that at least one child is a boy?

A. 1/2
B. 2/3
C. 3/4
D. 1/4

Solution

The only combinations with at least one boy are: BBB, BBG, BGB, GBB, BGG, GBG, GGB. Out of these, all combinations except BBB have at least one girl. Thus, P(At least one girl | At least one boy) = 6/7.

Correct Answer: B — 2/3

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Q. A family has 3 children. What is the probability that at least one of them is a girl given that at least one is a boy?

A. 1/2
B. 2/3
C. 3/4
D. 1

Solution

The only scenario where there are no girls is if all are boys. The probability of at least one girl given at least one boy is 3/4.

Correct Answer: C — 3/4

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Q. A jar contains 4 red, 5 green, and 6 blue marbles. If one marble is drawn at random, what is the probability that it is either red or green?

A. 4/15
B. 3/5
C. 9/15
D. 1/3

Solution

Total marbles = 4 + 5 + 6 = 15. Probability of red or green = (4 + 5)/15 = 9/15 = 3/5.

Correct Answer: B — 3/5

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Q. A jar contains 4 red, 5 green, and 6 blue marbles. If one marble is drawn at random, what is the probability that it is not green?

A. 1/3
B. 2/3
C. 1/2
D. 5/11

Solution

Total marbles = 4 + 5 + 6 = 15. Non-green marbles = 4 + 6 = 10. Probability = 10/15 = 2/3.

Correct Answer: B — 2/3

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Q. A jar contains 4 red, 5 green, and 6 blue marbles. If one marble is drawn at random, what is the probability that it is not blue?

A. 1/3
B. 2/3
C. 1/2
D. 5/11

Solution

Total marbles = 4 + 5 + 6 = 15. Non-blue marbles = 4 + 5 = 9. Probability = 9/15 = 3/5.

Correct Answer: B — 2/3

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Q. A jar contains 4 red, 5 green, and 6 blue marbles. What is the probability of drawing a green marble?

A. 1/3
B. 5/15
C. 5/15
D. 1/5

Solution

Total marbles = 4 + 5 + 6 = 15. Probability of green = 5/15 = 1/3.

Correct Answer: A — 1/3

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Q. A jar contains 4 red, 5 green, and 6 blue marbles. What is the probability of picking a green marble?

A. 5/15
B. 1/3
C. 1/5
D. 1/2

Solution

The total number of marbles is 4 + 5 + 6 = 15. The probability of picking a green marble is 5/15 = 1/3.

Correct Answer: B — 1/3

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Q. A jar contains 4 red, 5 green, and 6 blue marbles. What is the probability of randomly selecting a green marble?

A. 1/3
B. 5/15
C. 5/15
D. 1/5

Solution

The total number of marbles is 4 + 5 + 6 = 15. The probability of selecting a green marble is 5/15 = 1/3.

Correct Answer: A — 1/3

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Q. A jar contains 5 red, 3 green, and 2 blue marbles. If one marble is drawn at random, what is the probability that it is either red or green?

A. 1/2
B. 2/5
C. 4/5
D. 3/5

Solution

Total marbles = 5 + 3 + 2 = 10. Favorable outcomes (red or green) = 5 + 3 = 8. Probability = 8/10 = 4/5.

Correct Answer: C — 4/5

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Q. A jar contains 5 red, 3 green, and 2 blue marbles. What is the probability of drawing a green marble?

A. 1/5
B. 1/4
C. 3/10
D. 1/2

Solution

Total marbles = 5 + 3 + 2 = 10. Probability of green = 3/10.

Correct Answer: C — 3/10

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Q. A jar contains 5 red, 3 green, and 2 yellow marbles. If one marble is drawn at random, what is the probability that it is either red or green?

A. 1/2
B. 4/5
C. 2/5
D. 3/5

Solution

The total number of marbles is 5 + 3 + 2 = 10. The number of favorable outcomes (red or green) is 5 + 3 = 8. Thus, the probability is 8/10 = 4/5.

Correct Answer: B — 4/5

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Q. A student has a 70% chance of passing an exam. What is the probability that the student fails the exam?

A. 0.3
B. 0.7
C. 0.5
D. 0.2

Solution

The probability of failing the exam is 1 - 0.7 = 0.3.

Correct Answer: A — 0.3

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Q. A student is selected at random from a class of 40 students, where 25 are boys and 15 are girls. What is the probability that the student is a boy given that the student is not a girl?

A. 1/2
B. 3/4
C. 5/8
D. 2/5

Solution

If the student is not a girl, they must be a boy. Therefore, P(Boy | Not Girl) = 1.

Correct Answer: B — 3/4

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Q. A student is selected at random from a class of 40 students, where 25 are boys and 15 are girls. What is the probability that the student is a girl given that the student is not a boy?

A. 1/3
B. 1/2
C. 2/3
D. 3/4

Solution

The total number of students that are not boys is 15 (girls). The probability of selecting a girl given that the student is not a boy is 15/15 = 1.

Correct Answer: C — 2/3

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Q. A student is selected at random from a group of 40 students, where 25 are studying Mathematics and 15 are studying Physics. What is the probability that the student is studying Physics given that the student is not studying Mathematics?

A. 0
B. 1/3
C. 3/8
D. 1/2

Solution

If the student is not studying Mathematics, they must be studying Physics. Therefore, the probability is 1.

Correct Answer: B — 1/3

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Q. A student is selected at random from a group of 40 students, where 25 are studying Mathematics and 15 are studying Physics. What is the probability that the student is studying Mathematics given that they are not studying Physics?

A. 5/8
B. 3/8
C. 1/2
D. 1/3

Solution

If the student is not studying Physics, they must be studying Mathematics. Therefore, P(Math | Not Physics) = 1.

Correct Answer: A — 5/8

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Q. A student is selected at random from a group of students who study Mathematics and Physics. If 70% study Mathematics and 40% study both subjects, what is the probability that a student studies Physics given that they study Mathematics?

A. 0.4
B. 0.3
C. 0.5
D. 0.6

Solution

Using the formula P(Physics|Mathematics) = P(Physics and Mathematics) / P(Mathematics) = 0.4 / 0.7 = 0.571.

Correct Answer: A — 0.4

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Q. A student is selected from a class of 40 students, where 25 are girls and 15 are boys. What is the probability that the student is a girl given that the student is not a boy?

A. 1
B. 0
C. 1/2
D. 3/4

Solution

If the student is not a boy, they must be a girl. Therefore, the probability is 1.

Correct Answer: A — 1

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Q. Calculate the interquartile range (IQR) for the data set: 1, 3, 7, 8, 9, 10.

A. 4
B. 5
C. 6
D. 7

Solution

Q1 = 3, Q3 = 9; IQR = Q3 - Q1 = 9 - 3 = 6.

Correct Answer: A — 4

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Q. Calculate the mean absolute deviation for the data set: 1, 2, 3, 4, 5.

A. 1
B. 1.5
C. 2
D. 2.5

Solution

Mean = 3. Mean Absolute Deviation = (|1-3| + |2-3| + |3-3| + |4-3| + |5-3|)/5 = (2 + 1 + 0 + 1 + 2)/5 = 1.5.

Correct Answer: B — 1.5

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Q. Calculate the mean of the following data: 5, 10, 15, 20.

A. 10
B. 12.5
C. 15
D. 17.5

Solution

Mean = (5 + 10 + 15 + 20) / 4 = 50 / 4 = 12.5.

Correct Answer: B — 12.5

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Q. Calculate the mean of the following numbers: 10, 20, 30, 40, 50.

A. 30
B. 35
C. 40
D. 45

Solution

Mean = (10 + 20 + 30 + 40 + 50) / 5 = 150 / 5 = 30.

Correct Answer: A — 30

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Q. Calculate the mean of the following numbers: 4, 8, 12, 16, 20.

A. 10
B. 12
C. 14
D. 16

Solution

Mean = (4 + 8 + 12 + 16 + 20) / 5 = 60 / 5 = 12.

Correct Answer: C — 14

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Statistics & Probability

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