A bag contains 4 red, 3 white, and 5 blue bal | vedclass

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

Question

(A) Total number of balls = $4 + 3 + 5 = 12$.Total ways to draw $3$ balls = $^{12}C_3 = \frac{12 	imes 11 	imes 10}{3 	imes 2 	imes 1} = 220$.$(A)

Vedclass · Accepted Answer

Vedclass · Answer

(A) Total number of balls = $4 + 3 + 5 = 12$.Total ways to draw $3$ balls = $^{12}C_3 = \frac{12 	imes 11 	imes 10}{3 	imes 2 	imes 1} = 220$.$(A)$ Probability of getting $1$ red, $1$ white and $1$ blue ball:Ways = $^4C_1 	imes ^3C_1 	imes ^5C_1 = 4 	imes 3 	imes 5 = 60$.Probability = $\frac{60}{220} = \frac{3}{11}$ (Matches $(iv)$).$(B)$ Probability of getting $2$ white and $1$ blue ball:Ways = $^3C_2 	imes ^5C_1 = 3 	imes 5 = 15$.Probability = $\frac{15}{220} = \frac{3}{44}$ (Matches $(i)$).$(C)$ Probability of getting $2$ red and $1$ white ball:Ways = $^4C_2 	imes ^3C_1 = 6 	imes 3 = 18$.Probability = $\frac{18}{220} = \frac{9}{110}$ (Matches $(v)$).$(D)$ Probability that none of the balls is white (i.e.,all $3$ are from red and blue balls, total $4+5=9$):Ways = $^9C_3 = \frac{9 	imes 8 	imes 7}{3 	imes 2 	imes 1} = 84$.Probability = $\frac{84}{220} = \frac{21}{55}$ (Matches $(ii)$).Therefore, the correct matching is: $A ightarrow (iv), B ightarrow (i), C ightarrow (v), D ightarrow (ii)$.

List-$I$	List-$II$
$A$. Probability of getting $1$ red, $1$ white and $1$ blue ball	$(i)$ $\frac{3}{44}$
$B$. Probability of getting $2$ white and $1$ blue ball	$(ii)$ $\frac{21}{55}$
$C$. Probability of getting $2$ red and $1$ white ball	$(iii)$ $\frac{38}{55}$
$D$. Probability that none of the balls is white	$(iv)$ $\frac{3}{11}$
	$(v)$ $\frac{9}{110}$

Similar Questions

Two cards are drawn at random from a pack of $52$ cards. The probability that both are the cards of spade is

$A$ $5$-digit number is formed using the digits $1, 2, 3, 4, 5, 6,$ and $8$. What is the probability that the number has even digits at both ends?

Three persons $A, B$,and $C$ are to speak at a function. If they speak in a random order,what is the probability that $A$ speaks before $B$ and $B$ speaks before $C$?

Two numbers are selected at random from $1, 2, 3, \dots, 100$ and are multiplied. The probability,correct to two decimal places,that the product thus obtained is divisible by $3$ is:

$A$ class has $15$ boys and $5$ girls. Suppose $3$ students are selected at random from the class. The probability that there are $2$ boys and $1$ girl is

Vedclass Test Series

Exam Paper Generator

Online Exam Module