2023
Mathematics
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A bag contains 8 red balls and some white balls. If the probability of drawing a white ball is half of the probability of drawing a red ball then find the probability of drawing a red ball and a white ball if the balls are drawn without replacement.
A.
1/3
B.
2/9
C.
2/3
D.
8/33
Correct Answer: 8/33
Explanation
Let the number of white balls be n The number of red balls = 8 Now, the probability of drawing a white ball = n/n+8 The probability of drawing a red ball = 8/n+8 Since Pr(White ball) = 1/2 x Pr(Red ball) ∴n/(n + 8)= 1/2 × 8/(n + 8) = n/(n + 8) = 4/(n + 8) ∴n = 4 Number of white balls = 4 The possible number of outcomes = n + 8 = 4 + 8 = 12 Pr(Red ball and White ball) = Pr(Red ball) x Pr(White ball) Pr(Red ball) = 8/12 Pr(Red ball) = 4/11 Pr(Red ball and white ball) = 8/12 × 4/11 ∴ Pr(Red ball and white ball) = 8/33
Let the number of white balls be n The number of red balls = 8 Now, the probability of drawing a white ball = n/n+8 The probability of drawing a red ball = 8/n+8 Since Pr(White ball) = 1/2 x Pr(Red ball) ∴n/(n + 8)= 1/2 × 8/(n + 8) = n/(n + 8) = 4/(n + 8) ∴n = 4 Number of white balls = 4 The possible number of outcomes = n + 8 = 4 + 8 = 12 Pr(Red ball and White ball) = Pr(Red ball) x Pr(White ball) Pr(Red ball) = 8/12 Pr(Red ball) = 4/11 Pr(Red ball and white ball) = 8/12 × 4/11 ∴ Pr(Red ball and white ball) = 8/33THIS WEEK's
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