A bag contains 13 white and 7 black balls. 2 | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Total number of balls $= 13 + 7 = 20$.The total number of ways to draw $2$ balls from $20$ is given by the sample space $n(S) = {}^{20}C_{2} = \fr

Vedclass · Accepted Answer

$\frac{99}{190}$

Vedclass · Answer

(D) Total number of balls $= 13 + 7 = 20$.The total number of ways to draw $2$ balls from $20$ is given by the sample space $n(S) = {}^{20}C_{2} = \frac{20 	imes 19}{2 	imes 1} = 190$.For the balls to be of the same colour,they must either both be white or both be black.Number of ways to choose $2$ white balls from $13$ is ${}^{13}C_{2} = \frac{13 	imes 12}{2 	imes 1} = 78$.Number of ways to choose $2$ black balls from $7$ is ${}^{7}C_{2} = \frac{7 	imes 6}{2 	imes 1} = 21$.Total number of favorable outcomes $n(E) = 78 + 21 = 99$.Therefore,the probability $P(E) = \frac{n(E)}{n(S)} = \frac{99}{190}$.

$A$ bag contains $13$ white and $7$ black balls. $2$ balls are drawn at random. What is the probability that they are of the same colour?

Similar Questions

Fifteen persons,including $A$ and $B$,sit down at random at a round table. The probability that there are $4$ persons between $A$ and $B$ is

Three unbiased coins are tossed once. What is the probability of getting at most two heads?

Two coins are tossed. Find the probability that two heads are obtained.

$A$ five-digit number is formed by writing the digits $1, 2, 3, 4, 5$ in a random order without repetition. What is the probability that the number is divisible by $4$?

$2$ dice are thrown. Find the probability of getting a multiple of $3$ as the sum.

Vedclass Test Series

Exam Paper Generator

Online Exam Module