Question
Three boxes B1, B2, B3 contain red and green balls in
the ratio 1:1, 3:5, and 5:3 respectively. A box is selected at random and a ball is drawn. What is the probability that the selected ball is red?Solution
We are given:
- Three boxes: B1, B2, B3
- Each is equally likely to be chosen ⇒ P(B1) = P(B2) = P(B3) = 1/3
- Ball is drawn from the selected box
- Ratios of red to green balls:
- B1: 1 : 1 ⇒ Red = 1/2
- B2: 3 : 5 ⇒ Red = 3 / (3 + 5) = 3/8
- B3: 5 : 3 ⇒ Red = 5 / (5 + 3) = 5/8
= (1/3)·(1/2) + (1/3)·(3/8) + (1/3)·(5/8)
= (1/6) + (1/8) + (5/24) Now take LCM = 24:
- (1/6) = 4/24
- (1/8) = 3/24
- (5/24) = 5/24
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