Question

There are two boxes containing 5 white and 6 blue balls and 3 white and 7 blue balls respectively. If one of the boxes is selected at random and a ball is drawn from it, then the probability that the ball is blue is

Answer 1

The probability of drawing a blue ball from either of the two boxes selected at random is 61/110 or approximately 0.5545.

Step-by-step explanation:

To calculate the probability that the ball drawn is blue, we must consider the two different scenarios separately and then combine their probabilities, since one of the two boxes is chosen arbitrarily. In mathematics, especially probability theory, this is known as a mixed probability problem.

• Probability of selecting the first box: 1/2
• Probability of selecting a blue ball from the first box: 6/(5+6) = 6/11
• Probability of selecting the second box: 1/2
• Probability of selecting a blue ball from the second box: 7/(3+7) = 7/10

Using these probabilities, the overall probability of drawing a blue ball is the sum of the probabilities of drawing a blue ball from each box, each multiplied by the probability of selecting that box:

P(Blue ball) = P(First box) × P(Blue from first box) + P(Second box) × P(Blue from second box) = (1/2 × 6/11) + (1/2 × 7/10) = 3/11 + 7/20 = 61/110 or approximately 0.5545