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A box contains five balls of same size and shape. Three of them are purple coloured balls and two of them are pink coloured balls. Balls are drawn from the box one at a time. If a purple ball is drawn, it is not replaced. If a pink ball is drawn, it is replaced with another pink ball. First ball is drawn. What is the probability of getting a purple ball in the next draw?  *1 point1/212/2527/5023/50

Question

A box contains five balls of same size and shape. Three of them are purple coloured balls and two of them are pink coloured balls. Balls are drawn from the box one at a time. If a purple ball is drawn, it is not replaced. If a pink ball is drawn, it is replaced with another pink ball. First ball is drawn. What is the probability of getting a purple ball in the next draw?  *1 point1/212/2527/5023/50

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Solution

The problem can be broken down into two scenarios:

  1. The first ball drawn is purple.
  2. The first ball drawn is pink.

Let's calculate the probability for each scenario:

  1. If the first ball drawn is purple, there are now 2 purple balls and 2 pink balls left in the box. So, the probability of drawing a purple ball next is 2/4 = 1/2.

  2. If the first ball drawn is pink, it is replaced with another pink ball. So, there are still 3 purple balls and 2 pink balls in the box. The probability of drawing a purple ball next is 3/5.

Now, we need to calculate the total probability. The probability of the first ball being purple is 3/5, and the probability of the first ball being pink is 2/5. So, the total probability is:

(3/5 * 1/2) + (2/5 * 3/5) = 3/10 + 6/25 = 15/50 + 12/50 = 27/50.

So, the probability of getting a purple ball in the next draw is 27/50.

This problem has been solved

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