A genetic counselor informs a couple that there is a 20 prob

A genetic counselor informs a couple that there is a 20% probability of having a child with blue eyes, a 75% probability of having a brown-eyed child, and a 5% probability of having a child with green eyes. There is a 50% probability that the child will be a boy and a 50% probability that the child will be girl. Determine the joint pdf for eye color and gender under the assumption that eye color and gender are independent. List the values of this joint pdf(preferably as a table). Does the joint pdf that you computed in the previous equation satisfy the conditions for joint points?

Solution

probability of blue eyed is 0.2 probability of girl 0.5 probability of blue eyed girl will be 0.2 * 0.5 = 0.1 probability of blue eyed is 0.2 probability of boy 0.5 probability of blue eyed boy will be 0.2 * 0.5 = 0.1 Probability of brown eyed girl child is 0.75* 0.5= 0.375 Probability of brown eyed boy child is 0.75* 0.5= 0.375 Probability of green eyed girl child is 0.05* 0.5= 0.025 Probability of green eyed boy child is 0.05* 0.5= 0.025