You need to buy three books for your finance course this semester.You estimate that there is 60% chance of that you can buy any one of the books cheaper online than in the bookstore.If you define "number of the finance books that will be cheaper online" as a random variable, which set of probabilities would be used to form the probability distribution for this random variable?
A).064, .298, .422, .216
B).064, .288, .432, .216
C).064, .268, .452, .216
D).064, .238, .482, .216
E).238, .064, .216, .482

Question

Quizplus · Accepted Answer

The probability distribution for the random variable, which represents the number of finance books that will be cheaper online, can be calculated using the binomial distribution formula: $P(X=k) = \binom{n}{k}p^k(1-p)^{n-k}$, where $n=3$ (the number of trials/books), $p=0.6$ (the probability of success, i.e., finding a cheaper book online), and $k$ is the number of successes (books found cheaper online). Calculating for $k=0, 1, 2, 3$, we get:- For $k=0$: $P(X=0) = \binom{3}{0}(0.6)^0(0.4)^3 = 1 \times 1 \times 0.064 = 0.064$- For $k=1$: $P(X=1) = \binom{3}{1}(0.6)^1(0.4)^2 = 3 \times 0.6 \times 0.16 = 0.288$- For $k=2$: $P(X=2) = \binom{3}{2}(0.6)^2(0.4)^1 = 3 \times 0.36 \times 0.4 = 0.432$- For $k=3$: $P(X=3) = \binom{3}{3}(0.6)^3(0.4)^0 = 1 \times 0.216 \times 1 = 0.216$Thus, the correct set of probabilities is 0.064, 0.288, 0.432, 0.216, which matches option B.

You Need to Buy Three Books for Your Finance Course