Final answer:
To find the probabilities, consider the possible outcomes and calculate the desired probabilities using the concept of probability.
Step-by-step explanation:
To find the probability in each case, we need to consider the possible outcomes and the total number of outcomes. Assuming that the gender of each child is independent and equally likely, we can use the concept of probability to calculate the desired probabilities.
a. The probability of having all girls is 1/2 * 1/2 * 1/2 * 1/2 = 1/16.
b. The probability of having exactly two girls and two boys is calculated by considering the number of different arrangements of two girls and two boys out of four children. The number of ways this can happen is given by the binomial coefficient, which is 4! / (2! * 2!) = 6. The probability is then 6/16 = 3/8.
c. The probability of having at least one child who is a girl is the complement of the probability of having all boys. So it is 1 - (1/2 * 1/2 * 1/2 * 1/2) = 1 - 1/16
= 15/16.
d. The probability of having at least one child of each gender is the complement of the probability of having all boys or all girls. So it is 1 - 1/16 - 1/16 = 14/16
= 7/8.