1. Suppose that, instead of tossing a coin, the player in Exercise 25 draws up to five cards from a deck consisting only of three red and three black cards. The player wins as soon as the number of red cards exceeds the number of black cards and loses as soon as three black cards have been drawn. Does the tree diagram for the card game have the same shape as the tree diagram for the coin game? Is there any difference in the probability of winning? If so, which game has the greater probability of winning?
Refer to Exercise 25,
A coin is to be tossed at most five times. The tosser wins as soon as the number of heads exceeds the number of tails and loses as soon as three tails have been tossed. Use a tree diagram for this game to calculate the probability of winning.
2. Traits passed from generation to generation are carried by genes. For a certain type of pea plant, the color of the flower produced by the plant (either red or white) is determined by a pair of genes. Each gene is of one of the types C (dominant gene) or c (recessive gene). Plants for which both genes are of type c (said to have genotype cc) produce white flowers. All other plants-that is, plants of genotypes CC and Cc-produce red flowers. When two plants are crossed, the offspring receives one gene from each parent.
Genotype ______ Color
cc....................white
Cc .................... red
CC.................... red
(a) Suppose that you cross two pea plants of genotype Cc. What is the probability that the offspring produces white flowers? Red flowers?
(b) Suppose that you have a batch of red-flowering pea plants, of which 60% have genotype Cc and 40% have genotype CC. If you select one of these plants at random and cross it with a white-flowering pea plant, what is the probability that the offspring will produce red flowers?