Five balls are drawn from a bag containing 6 white and 4 black balls. What is the probu
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that 3 white and 2 black balls are drawn.
Answers
Answer:
10/21
Explanation:
a = no. of ways of drawing 3 W out of 6 are 6C3
b = no. of ways of drawing 2B out of 4 are 4C2
total balls are 10.
c = no. of ways of drawing 5 of any type out of 10 are 10C5
req probability = (a+b)÷c
Q-Five balls are drawn from a bag containing 6 white and 4 black balls. What is the probability that 3 white and 2 black balls are drawn?
A- 10/21 is the answer.
Given,
The number of black balls = 4
The number of white balls = 6
To Find,
The probability that 3 white and 2 black balls are drawn =?
Solution,
Total balls = 6 + 4 = 10
The total ways of drawing 5 balls out of 10 balls = 10C5
The total ways of drawing 5 balls out of 10 balls = (10*9*8*7*6)/(5*4*3*2*1)
The total ways of drawing 5 balls out of 10 balls = 252 ways'
The ways of drawing 3 white balls from 6 white balls = 6C3
The ways of drawing 3 white balls from 6 white balls = 6!/(3!*3!)
The ways of drawing 3 white balls from 6 white balls = (6*5*4)/(3*2*1)
The ways of drawing 3 white balls from 6 white balls = 20 ways
The ways of drawing 2 black balls from 4 white balls = 4C2
The ways of drawing 2 black balls from 4 white balls = 4!/(2!*2!)
The ways of drawing 2 black balls from 4 white balls = (4*3)/(2*1)
The ways of drawing 2 black balls from 4 white balls = 6 ways
The ways of drawing 3 white and 2 black balls = 6*20
The ways of drawing 3 white and 2 black balls = 120 ways
The probability that 3 white and 2 black balls are drawn = 120 / 252
The probability that 3 white and 2 black balls are drawn = 10/21
Hence, the probability that 3 white and 2 black balls are drawn is 10/21.