Conditional probability and Bayes' theorem — practice questions

Question 1 · difficulty L2 · understanding

A bag contains $(\mathrm{N}+1)$ coins -N fair coins, and one coin with 'Head' on both sides. A coin is selected at random and tossed. If the probability of getting 'Head' is $\frac{9}{16}$, then N is equal to:

• A. 5
• B. 7
• C. 8
• D. 9

Question 2 · difficulty L2 · understanding

The probabilities that players A and B of a team are selected for the captaincy for a tournament are 0.6 and 0.4 , respectively. If $A$ is selected the captain, the probability that the team wins the tournament is 0.8 and if B is selected the captain, the probability that the team wins the tournament is 0.7 . Then the probability, that the team wins the tournament, is :

• A. 0.74
• B. 0.76
• C. 0.72
• D. 0.78

Question 3 · difficulty L2 · understanding

Bag A contains 9 white and 8 black balls, while bag B contains 6 white and 4 black balls. One ball is randomly picked up from the bag B and mixed up with the balls in the bag A . Then a ball is randomly drawn from the bag A . If the probability, that the ball drawn is white, is $\frac{\mathrm{p}}{\mathrm{q}}, \operatorname{gcd}(\mathrm{p}, \mathrm{q})=1$, then $\mathrm{p}+\mathrm{q}$ is equal to

• A. 24
• B. 22
• C. 23
• D. 21

Question 4 · difficulty L2 · understanding

There are three bags $$X, Y$$ and $$Z$$. Bag $$X$$ contains 5 one-rupee coins and 4 five-rupee coins; Bag $$Y$$ contains 4 one-rupee coins and 5 five-rupee coins and Bag $$Z$$ contains 3 one-rupee coins and 6 five-rupee coins. A bag is selected at random and a coin drawn from it at random is found to be a one-rupee coin. Then the probability, that it came from bag $$\mathrm{Y}$$, is :

• A. $$\frac{1}{2}$$
• B. $$\frac{1}{3}$$
• C. $$\frac{5}{12}$$
• D. $$\frac{1}{4}$$

Question 5 · difficulty L2 · understanding

A company has two plants $$A$$ and $$B$$ to manufacture motorcycles. $$60 \%$$ motorcycles are manufactured at plant $$A$$ and the remaining are manufactured at plant $$B .80 \%$$ of the motorcycles manufactured at plant $$A$$ are rated of the standard quality, while $$90 \%$$ of the motorcycles manufactured at plant $$B$$ are rated of the standard quality. A motorcycle picked up randomly from the total production is found to be of the standard quality. If $$p$$ is the probability that it was manufactured at plant $$B$$, then $$126 p$$ is

• A. 54
• B. 66
• C. 56
• D. 64

Question 6 · difficulty L2 · understanding

Let Ajay will not appear in JEE exam with probability $\mathrm{p}=\frac{2}{7}$, while both Ajay and Vijay will appear in the exam with probability $\mathrm{q}=\frac{1}{5}$. Then the probability, that Ajay will appear in the exam and Vijay will not appear is :

• A. $\frac{9}{35}$
• B. $\frac{3}{35}$
• C. $\frac{24}{35}$
• D. $\frac{18}{35}$

Question 7 · difficulty L2 · understanding

Two marbles are drawn in succession from a box containing 10 red, 30 white, 20 blue and 15 orange marbles, with replacement being made after each drawing. Then the probability, that first drawn marble is red and second drawn marble is white, is

• A. $$\frac{4}{25}$$
• B. $$\frac{2}{3}$$
• C. $$\frac{2}{25}$$
• D. $$\frac{4}{75}$$

Question 8 · difficulty L2 · understanding

Bag A contains 3 white, 7 red balls and Bag B contains 3 white, 2 red balls. One bag is selected at random and a ball is drawn from it. The probability of drawing the ball from the bag A, if the ball drawn is white, is

• A. 1/4
• B. 1/3
• C. 3/10
• D. 1/9

Question 9 · difficulty L2 · understanding

When a missile is fired from a ship, the probability that it is intercepted is $${1 \over 3}$$ and the probability that the missile hits the target, given that it is not intercepted, is $${3 \over 4}$$. If three missiles are fired independently from the ship, then the probability that all three hit the target, is :

• A. $${3 \over 4}$$
• B. $${3 \over 8}$$
• C. $${1 \over 27}$$
• D. $${1 \over 8}$$

Question 10 · difficulty L2 · understanding

An experiment has 10 equally likely outcomes. Let A and B be two non-empty events of the experiment. If A consists of 4 outcomes, the number of outcomes that B must have so that A and B are independent is :

• A. 2, 4 or 8
• B. 3, 6 or 9
• C. 4 or 8
• D. 5 or 10