Algebra

Probability

Easy

core

A pair of dice is thrown, then the probability of getting a sum of 7, is

1/7

1/6

2/3

5/6

✅ Correct Option: 2

Two dice give 36 equally likely outcomes.

A sum of 7 occurs for $(1,6),(2,5),(3,4),(4,3),(5,2),(6,1)$ , that is 6 outcomes.

Probability $=\frac{6}{36}=\frac16$ .

2026: 31 May Shift 2

Match the LIST-I with LIST-II

	LIST-I		LIST-II
A.	If $A$ and $B$ are mutually exclusive events then $P(A \cup B) =$	I.	$\dfrac{P(A \cap B)}{P(B)}, P(B) \neq 0$
B.	If $A$ and $B$ are independent events then $P(A \cap B) =$	II.	$\dfrac{P(A \cap B)}{P(A)}, P(A) \neq 0$
C.	If $A$ and $B$ are two events of a sample space of an experiment, then $P(A/B) =$	III.	$P(A) \cdot P(B)$
D.	If $A$ and $B$ are two events of a sample space of an experiment, then $P(B/A) =$	IV.	$P(A) + P(B)$

Choose the correct answer from the options given below:

2025: 30 May Shift 2

If A and B are two events such that P(A) ≠ 0 and P(B | A) = 1 then

2025: 30 May Shift 1

The probability distribution of a random variable X is given by

X	0	1	2
P(X)	k	2k	3k

If k > 0, then $P(0 < X \leq 2)$ is equal to

2026: 25 May Shift 1

Bag A contains 3 red and 4 black balls, and Bag B contains 5 red and 'n' black balls. One ball is drawn at random from one of the bags and it is found to be red. If the probability that it was from bag B is 35/68, then the value of 'n' is:

2025: 19 May Shift 1

In 5 trials of binomial distribution, the probability of 3 successes is 4 times the probability of 2 successes. The probability of success in each trial is:

2025: 22 May Shift 2

The random variable X can take values 0, 1, 2. If $P(X=0)=P(X=1)=\alpha$ , and $E(X^2)=E(X)$ , then which of the following are correct?

(A) $E(X) = 2-3\alpha$

(B) $E(X^2) = 4+7\alpha$

(D) $\alpha = \frac{1}{5}$

Choose the correct answer from the options given below:

A pair of dice is thrown, then the probability of getting a sum of 7, is

Solution

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