A box contains 4 red and 6 blue balls. Two are drawn from this box one after the other. What is the probability that they are red,if first drawn ball is replaced?

Answer 1

Hi Ethan,

Since the first ball chosen is replaced, the two draws are independent of one another. So, the probability of getting two red balls is simply the probability of getting a red ball multiplied by the probability of getting a red ball.

The probability of getting a red ball is 4/10, or 0.4, since there are 10 balls total and 4 of them are red.

Therefore, the probability of getting two red balls is (0.4)(0.4) = 0.16 (or 16/100 which reduces to 4/25).

Hope this helps.

JMJ

Answer 2

For the first draw, the probability of drawing a red ball is 4/10 (4 red balls and 10 total balls). When you put the ball you drew back into the box, the second draw has the same probability as the first, 4/10.

The probability of two independent events occurring is the probability of one times the probability of the other so 4/10 * 4/10 = 16/100 or, reduced, 4/25