Algebra

Probability

Easy

common

A bag contains 8 red and 7 black balls. Two balls are drawn at random. The probability that both the balls are of the same colour is:

$\frac{14}{15}$

$\frac{11}{15}$

$\frac{7}{15}$

$\frac{4}{15}$

✅ Correct Option: 3

Total ways $= \binom{15}{2}=105$ .

Both red $=\binom{8}{2}=28$ ; both black $=\binom{7}{2}=21$ .

Favourable $=28+21=49$ , so probability $=\frac{49}{105}=\frac{7}{15}$ .

2025: 27 May Shift 1

Let X be a random variable. Let E (X) and Var (X) denote the mean and the variance of X respectively. Then match List-I with List-II

List-I	List-II
(A) If Var (X) = $a$ , then Var (2X + 3) is	(I) 11 $a$
(B) If E (X) = $a$ , then E (2X) is	(II) 6 $a$
(C) If Var (X) = $a$ , then Var(3X - $a$ ) + Var ( $\sqrt{2}x + \beta$ ) is	(III) 4 $a$
(D) If E (X) = $\frac{5a}{12}$ , then E (12X + $a$ ) is	(IV) 2 $a$

Choose the correct answer from the options given below:

2022: 23 Aug Shift 1

The probability that he copied it given that his answer is correct :

2026: 19 May Shift 2

A coin is tossed four times. The probability of getting atleast 1 head before getting the first tail is

2025: 22 May Shift 2

Two cards are drawn successively with replacement from a well-shuffled deck of 52 cards. The probability distribution of number of aces is given by:

2022: 4 Aug Shift 1

When the doctor arrives late, what is the probability that he comes by cab?

2025: 13 May Shift 2

A man is known to speak truth 3 out of 4 times. He throws a die and reports that it is four. The probability that it is actually four is

Solution