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

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

Question

(A) Total number of balls = $3 + 4 + 5 = 12$. Total ways to draw $2$ balls from $12$ is $^{12}C_2 = \frac{12 	imes 11}{2} = 66$. To find the probabil

Vedclass · Accepted Answer

$\frac{47}{66}$

Vedclass · Answer

(A) Total number of balls = $3 + 4 + 5 = 12$. Total ways to draw $2$ balls from $12$ is $^{12}C_2 = \frac{12 	imes 11}{2} = 66$. To find the probability that the balls are of different colors,it is easier to calculate the probability that they are of the same color and subtract it from $1$. Ways to draw $2$ balls of the same color: $(i)$ Both red: $^3C_2 = 3$ $(ii)$ Both white: $^4C_2 = 6$ $(iii)$ Both blue: $^5C_2 = 10$ Total ways to draw $2$ balls of the same color = $3 + 6 + 10 = 19$. Probability of same color = $\frac{19}{66}$. Probability of different colors = $1 - \frac{19}{66} = \frac{66 - 19}{66} = \frac{47}{66}$.

$A$ bag contains $3$ red,$4$ white,and $5$ blue balls. All balls are distinct. Two balls are drawn at random. The probability that they are of different colors is

Similar Questions

$A$ box contains $50$ tickets numbered $1, 2, 3, \dots, 50$. Five tickets are drawn at random and arranged in ascending order $(x_1 < x_2 < x_3 < x_4 < x_5)$. What is the probability that $x_3 = 30$?

If a coin is tossed seven times,then the probability of getting exactly three heads such that no two heads occur consecutively is

An urn contains nine balls of which three are red,four are blue and two are green. Three balls are drawn at random without replacement from the urn. The probability that the three balls have different colours is

The coefficients $a, b, c$ in the quadratic equation $ax^2 + bx + c = 0$ are chosen from the set $\{1, 2, 3, 4, 5, 6\}$. If the probability of this equation having two distinct real roots is $p$,then $216p$ equals:

If three distinct numbers are chosen randomly from the first $100$ natural numbers,then the probability that all three of them are divisible by both $2$ and $3$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module