10. A couple plans to have four children. If we consider only the gender of the children, having 4 children is much like flipping a coin 4 times. There are 16 possible outcomes, and all can be assumed to be equally likely. b. Use the multiplication rule to determine the probability for each of these outcomes, and write these probabilities to the right of the outcomes listed in the event tree. C. For each value X = # of girls out of 4 births, write the number of different outcomes (combinations) that result in that value of X in the Table below. Sample space of X 0 2 3 4 # Combinations P[X] d. Use the addition rule to determine the probability associated with each value of X, based on the probabilities of outcomes and the number of combinations that result in each value of X. Enter these probability values in the Table above e. Determine probabilities for the following events. Show your work by listing all values of X that meet the specified criterion, and sum the probabilities. The probability that the couple will have at least 1 girl The probability that the couple will have 2 girls The probability that the first child is a girl