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

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(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

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