stats and probability

(a) P(A n 3) Recall the Multiplication Rule for Independent Events, A and 3, gives the probability of their intersection, P(A n B), as follows. P(A n B) = P(A)P(B) We are given that P(A) = 0.5 and P(B) = 0.1. Substitute these values in the above equation to find P(A n B). P(A n B) = P(A)P(B) (0-5)( :1) A sample space 5 consists of ve simple events with these probabilities. P(E1) = P(E2) = 0.2 P(E3) = 0.45 P(E4) = 2P(E5) (a) Find the probabilities for simple events E4 and E5. P(E4) = 0.1 P(E5) = 0.05 (b) Find the probabilities for these two events. A = {E1, E3, E4} B = {[52, E3} P(A) = 0.75 P(B) = 0.65 (c) List the simple events that are either in event A or event B or both. (If there are no simple events, enter NONE.) { } (d) List the simple events that are in both event A and event B. (If there are no simple events, enter NONE.) { x} Five cards are selected from a 52-card deck for a poker hand. (a) How many simple events are in the sample space? 2,598,560 X simple events (b) A royal ush is a hand that contains the A, K, Q, J, and 10, all in the same suit. How many ways are there to get a royal flush? 4 ways (c) What is the probability of being dealt a royal flush? (Enter your probability as a fraction.) 4/2598560 x