Question

Your English teacher has decided to randomly assign poems for the class to read. The syllabus includes four poems by Shakespeare, five poems by Coleridge, two poems by Tennyson, and two poems by Lord Byron. What is the probability that you will be assigned a poem by Shakespeare, and then a poem by Tennyson?

Answer 1

P(A B) = P(A) P(B|A) denotes the chance of both events A and B occurring. It is the probability of Event A occurring multiplied by the probability of Event B occurring given that Event A has occurred. So, to determine the probability that you will be assigned a Shakespeare poem and a Tennyson poem, let Event A = the event that you will be assigned a Shakespeare poem and Event B = the event that you will be assigned a Tennyson poem. Initially, your class will be given a total of 13 poems at random. Shakespeare wrote four plays, so P(A) is 4/13. There would be 13 poems after the first pick. As a result, P(B|A) = 2/12. According to the multiplication formula, P(A B) = P(A) P(B|A)P(A B) = 4/13 * 2/12 P(A B) = 8/156 P(A B) = 2/39 The likelihood of being given a Shakespeare poem followed by a Tennyson poem is 2/39, or 5.13%.

Answer 2

The probability of event A and B to both occur is denoted as P(A ∩ B) = P(A) P(B|A). It is the probability that Event A occurs times the probability that Event B occurs, given that Event A has occurred.

So, to find the probability that you will be assigned a poem by Shakespeare and by Tennyson, let Event A = the event that a Shakespeare poem will be assigned to you; and let Event B = the event that the second poem that will be assigned to you will be by Tennyson.

At first, there are a total of 13 poems that would be randomly assigned in your class. There are 4 poems by Shakespeare, thus P(A) is 4/13.
After the first selection, there would be 13 poems left. Therefore, P(B|A) = 2/12
Based on the rule of multiplication,
P(A ∩ B) = P(A) P(B|A)P(A ∩ B) = 4/13 * 2/12
P(A ∩ B) = 8/156
P(A ∩ B) = 2/39

The probability that you will be assigned a poem by Shakespeare, then a poem by Tennyson is 2/39 or 5.13%.