On a game show, a contestant has to match a price with a prize they wish...

On a game show, a contestant has to match a price with a prize they wish to win. The prizes are a sports car and a boat. Of the four different price options, one is the price for the sports car, one is the price for the boat and two prices are incorrect. The contestant chooses one prize and matches it up with one price. Create a probability tree that shows all possible selections the contestant can make and calculate the probability of each of these selections. Lastly, determine what is the theoretical probability that the contestant will win the car, will win the boat, or will not win either prize.

Solutions

Expert Solution

The contestant will first select a prize that they wish to win. There are two prizes (a sports car and a boat). The contestant will select one of the prizes with equal probability. Therefore, for each prize the probability that the contestant selects that prize will be 0.5.

There are four prize options to match in which one option is a sports car, one is a boat and two are incorrect. Therefore, Probability of selecting the sports car is 1/4 = 0.25; Probability of selecting the boat is 1/4 = 0.25 and Probability of selecting incorrect prize is 2/4 = 0.5.

The contestant will first select a prize and then select an option to match the prize.

The tree diagram for whether a contestant will win a Prize or not is as follows,

Probability that the contestant will win a car = P(Prize = Sports Car)*P(Option = Sports car) = 0.5*0.25 = 0.125.

Probability that the contestant will win a boat = P(Prize = Boat)*P(Option = Boat) = 0.5*0.25 = 0.125.

Probability that the contestant will not win either prize = {P(Prize = Sports Car)*[P(Option = boat+P(Option = Incorrect))]}+{P(Prize = Boat)*[P(Option = Sports Car)+P(Option = Incorrect)]}

= [0.5(0.25+0.5)]+[0.5(0.25+0.5)] = (0.5*0.75)+(0.5*0.75) = 0.375 + 0.375 = 0.75.

Do comment for any doubts.

orchestra answered 1 year ago

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