The probability that a child will learn to swim before age 6 is 0.312. If you take a group of 12 children, what is the probability that 1 or fewer of the children will learn to swim before age 6? (Round your answer to 3 decimal places if necessary.)

The probability of 1 or less children from that group to learn how to swim before 6 years of age is 0.072

Step-by-step explanation:

In this case we need to compute the probability of none of these 12 children learns to swim before 6 years of age. This is given by:

p (0) = (1 - 0.312) ^ (12) = 0.688^ (12) = 0.01124

We now need to calculate the probability that one child learns to swim before 6 years of age.

p (1) = 12*0.312 * (1 - 0.312) ^ (11) = 3.744 * (0.688) ^ (11)

p (1) = 3.744*0.01634

p (1) = 0.0612

The probability of 1 or less children from that group to learn how to swim before 6 years of age is:

p = p (0) + p (1) = 0.01124 + 0.0612 = 0.07244