In a group of computer engineering students, some like algebra and others do not like algrebra. There is no student in this group who is indifferent or has no opinion. Two students are randomly selected from this group. (a) How many outcomes are possible? List all the possible outcomes. (b) Consider the following events. List all the outcomes included in each of these events. Mention whether each of these events is a simple or a compound event. (i) Both students like algebra. (ii) At most one student likes algebra. (iii) At least one student likes algebra. (iv)Neither student likes algebra.

Solution.

(a)

There are four possible outcomes in this situation: LL, LD, DL and DD,

where L - outcome, where student like algebra, D - outcome, where student dislike algebra.

(b)

(i)

There is one possible outcome in this situation: LL, where L - outcome, where student like algebra. It is a simple event.

(ii)

There are three possible outcomes in this situation: LD, DL and DD,

where L - outcome, where student like algebra, D - outcome, where student dislike algebra. It's a compound event.

(iii)

There are three possible outcomes in this situation: LL, LD and DL,

where L - outcome, where student like algebra, D - outcome, where student dislike algebra. It's a compound event.

(iv)

There is one possible outcome in this situation: DD, where D - outcome, where student dislike algebra. It is a simple event.