Algebra

Probability

Medium

core

A bag contains 4 red and 6 black balls. Two balls are drawn in succession without replacement. The probability that the first is red and the second is black is

$\frac{2}{5}$

$\frac{2}{3}$

$\frac{4}{15}$

$\frac{6}{25}$

✅ Correct Option: 3

The bag contains:

4 red balls
6 black balls
Total = 10 balls

Two balls are drawn in succession without replacement.

When the first ball is drawn, there are 10 balls total with 4 red balls.

$P(\text{First ball is Red}) = \frac{4}{10}$

After drawing one red ball, the bag contains:

3 red balls
6 black balls
Total = 9 balls

$P(\text{Second ball is Black | First was Red}) = \frac{6}{9}$

For both events to occur:

$P(\text{Red first AND Black second}) = \frac{4}{10} \times \frac{6}{9}$

$= \frac{24}{90}$

$= \frac{4}{15}$

Therefore, the probability is $\frac{4}{15}$ .

2025: 21 May Shift 2

If $X$ is a random variable which can assume values $0, 1, 2, 3$ or $4$ such that $P(X = 1) = P(X = 2)$ and $3P(X = 3) = 4P(X = 4) = P(X = 0) = \frac{1}{8}$ , then $P(X > 0)$ is:

2025: 29 May Shift 2

Match List-I with List-II

If the random variable x has the following distribution:

x	0	1	2	otherwise
P(x)	k	k	2k	0

List-I	List-II
(A) k	(I) $\frac{3}{4}$
(B) P(x ≥ 2)	(II) $\frac{1}{4}$
(C) P(x ≤ 2)	(III) $\frac{1}{2}$
(D) P(0 < x ≤ 2)	(IV) 1

Choose the correct answer from the options given below:

2022: 23 Aug Shift 1

If a fair coin is tossed 10 times, then the probability of getting all heads or all tails, is :

2025: 21 May Shift 2

The probability that it will rain on any particular day is 50%. The probability that it rains only on the first 4 days of the week is:

2025: 15 May Shift 2

If the probability that an individual suffers a bad reaction from an injection of a given serum is 0.001. The probability that out of 2000 individuals, more than two individuals suffer from bad reaction is:

[Given that $e^{-2} \approx 0.13534$ ]

2025: 3 June Shift 1

A random variable X has the following probability distribution:

X	2	3	4	5
P(X)	5/k	7/k	9/k	11/k

Then the value of $\frac{k}{4}$ is:

A bag contains 4 red and 6 black balls. Two balls are drawn in succession without replacement. The probability that the first is red and the second is black is

Solution

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