Algebra

Probability

Medium

common

Three balls are drawn one by one without replacement from a bag containing 5 white and 4 red balls. Let X denote the number of white balls.

Match the LIST-I with LIST-II

LIST-I LIST-II
A. $P(X=0)$ I. $10/21$
B. $P(X=1)$ II. $5/42$
C. $P(X=2)$ III. $1/21$
D. $P(X=3)$ IV. $5/14$

Choose the correct answer from the options given below:

LIST-I	LIST-II
A. $P(X=0)$	I. $10/21$
B. $P(X=1)$	II. $5/42$
C. $P(X=2)$	III. $1/21$
D. $P(X=3)$	IV. $5/14$

A-III, B-II, C-IV, D-I

A-I, B-II, C-IV, D-III

A-III, B-IV, C-I, D-II

A-IV, B-III, C-II, D-I

✅ Correct Option: 3

Total selections $=\binom{9}{3}=84$ . Then $P(X=0)=\frac{\binom{4}{3}}{84}=\frac{1}{21}$ (III), $P(X=1)=\frac{5 \times \binom{4}{2}}{84}=\frac{30}{84}=\frac{5}{14}$ (IV), $P(X=2)=\frac{\binom{5}{2}\times 4}{84}=\frac{40}{84}=\frac{10}{21}$ (I), and $P(X=3)=\frac{\binom{5}{3}}{84}=\frac{5}{42}$ (II).

2026: 19 May Shift 2

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

2022: 17 Aug Shift 2

If $A$ and $B$ are independent events such that $0 < P(A) < 1$ and $0 < P(B) < 1$ , then identify the correct statements.

(A) $A$ and $B'$ are independent

(B) $A'$ and $B$ are independent

(D) $A'$ and $B'$ are independent

Choose the correct answer from the options given below :

2025: 14 May Shift 1

The probability distribution of a random variable X is given by

X	0	1	2
P(X)	$1 - 7a^2$	$\frac{1}{2}a + \frac{1}{4}$	$a^2$

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

2026: 14 May Shift 2

A pair of coins thrown then

Match the LIST-I with LIST-II

	LIST-I		LIST-II
A.	Probability of occurance of head on both coins is	I.	$\dfrac{3}{4}$
B.	Probability of occurance of at least one tail is	II.	$\dfrac{1}{2}$
C.	Probability of occurance of one tail only is	III.	$1$
D.	Probability of a tail appears on one coin given that only one coin shows head.	IV.	$\dfrac{1}{4}$

Choose the correct answer from the options given below:

2022: 25 May Shift 1

In a meeting, 70% of the members favour and 30% oppose a certain proposal. A member is selected at random and we take X = 0 if he opposed, and X = 1 if he is in favour. Then, E (X) is :

2022: 4 Aug Shift 1

If two numbers are selected at random from the first 25 natural numbers, then the probability that their sum will be odd is:

Solution

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