Question

Your English teacher has decided to randomly assign poems for the class to read. The syllabus includes 2 poems by Shakespeare, 3 poems by Coleridge, 5 poems by Tennyson, and 4 poems by Lord Byron. What is the probability that you will be assigned a poem by Coleridge and then a poem by Lord Byron?

Answer 1

The probability of being assigned a poem by Coleridge and then by Lord Byron is calculated by multiplying the individual probabilities: (3/14) for Coleridge and (4/13) for Byron, yielding a combined probability of approximately 0.066.

Step-by-step explanation:

The probability of being assigned a poem by Coleridge followed by one by Lord Byron involves calculating the probability of two independent events. The total number of poems is 2 (Shakespeare) + 3 (Coleridge) + 5 (Tennyson) + 4 (Lord Byron) = 14.

The probability of first getting a Coleridge poem is 3/14 since there are 3 out of 14 that are by Coleridge.

Assuming one poem is already taken, there will be 13 poems left and 4 of them are by Lord Byron, so the probability of then getting a Byron poem is 4/13.

To find the combined probability, these are multiplied together: (3/14) × (4/13) = 12/182 = 1/15.17 or approximately 0.066.

Answer 2

`|\Omega|=14\cdot13=182\\ |A|=3\cdot4=12\\\\ P(A)=(12)/(182)=(6)/(91)`