Question

2. Suppose A represents Serena being selected, and B represents Dominic (another student in class) being selected.The event Al means Serena was selected on Monday, and the event B2 means Dominic was selected on TuesdayThe event B1 means Dominic was selected on Monday, and the event A2 means Serena was selected on Tuesdaya. Explain in words what P(A1 and B2) represents, and then calculate this probabilityb.Explain in words what P(B1 and A2) represents, and then calculate this probability

Answer 1

All the events of the statement are independent events, so in order to calculate the probability of two events ocurring at the same time, we just need to calculate the product of the probabilities of the individual events.

An example (of notation):

P(A1) = probability of Serena being selected on monday

a. P(A1 and B2) = is the probability of Serena being selected on Monday AND Dominic being selected on Tuesday

We can calculate this probability in the following way:

P(A1 and B2) = P(A1) * P(B2)

b. P(B1 and A2) = is the probability of Dominic being selected on Monday AND Serena being selected on Tuesday

As before, because the events are independent, we can calculate the probability in the following way:

P(B1 and A2) = P(B1) * P(A2)

Note: it is important to remember the rule that we can multiply probabilities (of events) when they are independent.