uppose that you throw a fair six-sided die (with an equal probability of getting numbers 1 through 6), and consider two events: (i) the number on the top is an odd number (O = {1, 3, 5}) and (ii) the number on the top is three or smaller (S = {1, 2, 3}).  What is P(O ∩ S), i.e. the probability that the two events happen simultaneously?

Two players, A and B, alternately and independently flip a coin for a game. The game has up to a total of 5 flips and the first player to obtain a head wins. Assume player A flips first. The coin is unfair with P(head) = 2/3. Find the probability that player A wins

If P (Event A)=0.2 and P(Event B)=0.3, and the two events are disjoint, then P (Event A and Event B) is?

At a local​ college, four sections of economics are taught during the day and two sections are taught at night. 65 percent of the day sections are taught by​ full-time faculty. 15percent of the evening sections are taught by​ full-time faculty. If Jane has a​ part-time teacher for her economics​ course, what is the probability that she is taking a night​ class? The probability that she is taking a night class is nothing. ​(Type an integer or a​ fraction.)

Let A and B be two events with P(A and Bc) = 1. Find P(B). Recall that Bc denotes the complement of the event B.

The yellow and green dice are tossed together. If A is the event that a 2 is shown on the yellow die and B is the event that 3 is shown on the green die, thena) determine P(A), P(B)b) Find the probability of getting a 2 on the yellow die and a 4 on the green.