Find the probability of drawing two red balls in succession from a bag containing 3 red and 6 black balls when (i) the ball is draw first is replaced (ii) it is not replaced
Answers
Answer:
(i) 1/9
(ii) 1/12
Step-by-step explanation:
(i) probability of drawing 2 red balls uf the ball is draw first is replaced=3/9*3/9
=1/9
(ii) probability of drawing 2 red balls if it is not replaced =3/9*2/8
=1/12
Given,
The number of red balls = 3
The number of black balls = 6
To Find,
The probability of drawing two red balls in succession from a bag when the first ball is replaced =?
The probability of drawing two red balls in succession from a bag when the first ball is not replaced =?
Solution,
Total balls = number of red balls + number of black balls
Total balls = 3 + 6
Total balls = 9
The probability of drawing a red ball = The number of red balls / Total balls
The probability of drawing a red ball = 3 / 9
The probability of drawing a red ball = 1 / 3
The probability of drawing a second red ball if the ball is replaced = 3 / 9= 1/3
The probability of drawing two red balls in succession from a bag when the first ball is replaced = (1 / 3) * (1 / 3) = 1 / 9
If the ball is not replaced for second time,
The number of red balls = 3 - 1 = 2
Total balls = 9 - 1 = 8
The probability of drawing a second red ball if the ball is not replaced=2/8
The probability of drawing a second red ball if the ball is not replaced=1/4
The probability of drawing two red balls in succession from a bag when the first ball is not replaced = (1 / 3) * (1 / 4)
The probability of drawing two red balls in succession from a bag when the first ball is not replaced = 1 / 12
Hence, the probability of drawing two red balls in succession from a bag containing 3 red and 6 black balls when the first drawn ball is replaced is 1/9 and the probability of drawing two red balls in succession from a bag containing 3 red and 6 black balls when the first drawn ball is not replaced is 1/12.