Mathematics
Mathematics
Problem
A bag contains 4 white and 6 black balls. Two balls are drawn successively with replacement. Calculate the probability that both balls drawn are white.Intuitive explanation
When you draw with replacement, each draw is independent—the first ball goes back in before you draw the second. This means the probability of drawing white stays the same for both draws. The key insight is to multiply the individual probabilities together: if each draw has the same chance of success, the probability of both succeeding is just that chance squared (or the product of the two identical probabilities).
Intuitive explanation
When you draw with replacement, each draw is independent—the first ball goes back in before you draw the second. This means the probability of drawing white stays the same for both draws. The key insight is to multiply the individual probabilities together: if each draw has the same chance of success, the probability of both succeeding is just that chance squared (or the product of the two identical probabilities).