In a game, a box has balls numbered 2 - 51. A person wins a soft toy if the number on the ball picked is a prime number and gets nothing if the number is a composite number. A ball is picked and replaced. Find the probability if a person gets a soft toy on the first and second draw, and gets nothing in the third draw.

The balls are numbered 2 through 51, giving a total of 50 balls. The prime numbers in this range are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, and 47, totaling 15 primes, so the probability of drawing a prime is 15/50, or 0.3. There are 50 total balls minus the 15 prime balls, leaving 35 composite balls, making the probability of drawing a composite 35/50, or 0.7. For the independent events of getting a prime, another prime, and then a composite, we multiply their probabilities: 0.3 multiplied by 0.3 multiplied by 0.7. The result is 0.063, which equals 63/1000.

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