Bag A contains 3 red and 5 white balls and bag B contains 4 red and 4 white balls. A bag is selected at random, and a ball is drawn. Then the probability of getting a red ball is: Option 1: less than 0.33 Option 2: more than 0.33 but less than 0.50 Option 3: more than 0.5 but less than 0.67 Option 4: more than 0.67

Answer: more than 0.33 but less than 0.50. Solution: Each bag is equally likely, so by total probability: P(red) = 1/2x3/8 + 1/2x4/8 = 3/16+4/16 = 7/16. This equals 0.4375, which lies between 0.33 and 0.50.

Algebra

Probability

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Bag A contains 3 red and 5 white balls and bag B contains 4 red and 4 white balls. A bag is selected at random, and a ball is drawn. Then the probability of getting a red ball is:

less than 0.33

more than 0.33 but less than 0.50

more than 0.5 but less than 0.67

more than 0.67

✅ Correct Option: 2

Each bag is equally likely, so by total probability:

$P(\text{red}) = \dfrac{1}{2}\times\dfrac{3}{8} + \dfrac{1}{2}\times\dfrac{4}{8} = \dfrac{3}{16}+\dfrac{4}{16} = \dfrac{7}{16}$ .

This equals $0.4375$ , which lies between $0.33$ and $0.50$ .

2026: 30 May Shift 2

A random variable X has the following probability distribution:

X	0	1	2	3	4	5	6
P(X)	z	2z	2z	3z	$z^2$	$2z^2$	$7z^2+z$

Which of the following are TRUE?

(A) P(X < 3) = 0.8

(B) P(X > 4) = 0.2

(D) $P(3\le X<5) = 0.31$

Choose the correct answer from the options given below:

2026: 21 May Shift 1

A problem is given to 3 students A,B and C, whose probabilities of solving are $\frac{1}{2}, \frac{1}{3}$ and $\frac{1}{4}$ respectively, then

(A). P(Problem solved) = $\frac{3}{4}$

(B). P(Problem not solved) = $\frac{1}{4}$

(C). P(Problem solved by exactly one student) = $\frac{7}{24}$

(D). P(Problem solved by at least 2 students) = $\frac{17}{24}$

Choose the correct answer from the options given below:

2026: 30 May Shift 1

A box has 5 blue and 4 red balls. One ball is drawn at random and not replaced. Its colour is also not noted, then another ball is drawn at random. The probability of second ball being red is

2025: 15 May Shift 1

If a computer code is correctly programmed, it gives 90% acceptable results. But if it is not correctly programmed, it gives only 40% acceptable results. From previous experience, it is observed that only 80% of codes are correctly programmed. If after a certain programming, the code gives 2 acceptable results, then the approximate probability that the code is correctly programmed is

2025: 30 May Shift 1

A random variable y has the following probability distribution

y	1	2	3	4	5
P(y)	2k	3k	k	4k	5k

Match List-I with List-II

List-I	List-II
(A) $P(y > 2)$	(I) $2/5$
(B) k	(II) $2/3$
(C) $P(y \leq 3)$	(III) $8/15$
(D) $P(2 \leq y \leq 4)$	(IV) $1/15$

Choose the correct answer from the options given below:

2022: 25 May Shift 1

Probabilities to solve a specific problem by A, B and C are $\frac{1}{2}, \frac{1}{3}$ and $\frac{1}{4}$ respectively. Probability that at least one will solve the problem is:

Bag A contains 3 red and 5 white balls and bag B contains 4 red and 4 white balls. A bag is selected at random, and a ball is drawn. Then the probability of getting a red ball is:

Solution

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