Use the list and calculation method to answer the following questions. Show your work at each step.
4. You draw three cards (with replacement) from a standard deck of cards. What is the probability that
a. exactly one will be red: .125 + .125 + .125 = .375
b. none will be red, and: .125
c. more than two will be red: .125
Outcome Probability No. of Hits
RRR (.5)(.5)(.5) = .125 3
RRB (.5)(.5)(.5) = .125 2
RBR (.5)(.5)(.5) = .125 2
RBB (.5)(.5)(.5) = .125 1
BRR (.5)(.5)(.5) = .125 2
BRB (.5)(.5)(.5) = .125 1
BBR (.5)(.5)(.5) = .125 1
BBB (.5)(.5)(.5) = .125 0
To calculate the probability of drawing cards from a standard deck, we can use the list and calculation method. Let's go through each question and calculate the probability step by step.
a. Exactly one card will be red:
To calculate the probability of exactly one card being red, we need to consider the different outcomes. There are three possibilities: RBB, BRB, and BBR. Each outcome has the same probability, which is (0.5)(0.5)(0.5) = 0.125. So, we add these three outcomes' probabilities together: 0.125 + 0.125 + 0.125 = 0.375. Therefore, the probability that exactly one card will be red is 0.375.
b. None of the cards will be red:
To calculate the probability of none of the cards being red, we need to consider the outcome BBB. The probability of this outcome is (0.5)(0.5)(0.5) = 0.125. Therefore, the probability that none of the cards will be red is 0.125.
c. More than two cards will be red:
To calculate the probability of more than two cards being red, we need to consider the outcomes RRR, RRB, RBR, BRR. Each outcome has the same probability, which is (0.5)(0.5)(0.5) = 0.125. Therefore, the probability that more than two cards will be red is 0.125.