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There are two boxes containing 5 white and 6 blue balls and 3 white and 7 blue balls respectively. If one of the the boxes is selected at random and a ball is drawn from it, then the probability that the ball is blue is
  • a)
    115/227
  • b)
    83/250
  • c)
    137/220
  • d)
    127/250
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
There are two boxes containing 5 white and 6 blue balls and 3 white an...
Given:
- Two boxes containing balls
- Box 1: 5 white and 6 blue balls
- Box 2: 3 white and 7 blue balls
- One box is selected at random and a ball is drawn from it

To find:
The probability that the ball drawn is blue

Solution:

Total number of balls in Box 1 = 5 + 6 = 11
Total number of balls in Box 2 = 3 + 7 = 10

Total number of balls in both boxes = 11 + 10 = 21

Probability of selecting Box 1 = 1/2
Probability of selecting Box 2 = 1/2

Using conditional probability,
P(blue ball) = P(blue ball | Box 1) × P(Box 1) + P(blue ball | Box 2) × P(Box 2)

Probability of drawing a blue ball from Box 1 = 6/11
Probability of drawing a blue ball from Box 2 = 7/10

Substituting the values,
P(blue ball) = (6/11) × (1/2) + (7/10) × (1/2)
P(blue ball) = 3/11 + 7/20
P(blue ball) = (60 + 77)/220
P(blue ball) = 137/220

Therefore, the probability that the ball drawn is blue is 137/220.
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There are two boxes containing 5 white and 6 blue balls and 3 white an...
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There are two boxes containing 5 white and 6 blue balls and 3 white and 7 blue balls respectively. If one of the the boxes is selected at random and a ball is drawn from it, then the probability that the ball is blue isa)115/227b)83/250c)137/220d)127/250Correct answer is option 'C'. Can you explain this answer?
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