Question

A student can study 1 or 2 hours for an astronomy test on any given night. However he is twice as likely to study one hour as he is to study two hours.

a. Write the sample space to show the different ways in which the student can study on three consecutive nights.

b. What is the probability that the student will study at least five hours on the three consecutive nights?

Answer 1

Here the student can study either 1 hour or 2 hour on any given night.

Here,

P(One hour) = 2 * P(Two hour)

as We know that

P(One hour) + P(Two hour) = 1

P(One hour) = 2/3

P(Two hour) = 1/3

(a) sample space on different ways in which the student can study on three consecutive nights.

S = {(1,1,1), (1,1,2), (1,2,1), (1,2,2), (2,1,1), (2,1,2), (2,2,1), (2,2,2)}

Here he will study atleast five hours when there is possiblites of (2,1,2), (2,2,1) or (2,2,2)

P(2,1,2) = 1/3 * 2/3 * 1/3 = 2/27

P(2,2,1) = 1/3 * 1/3 * 2/3 = 2/27

P(2,2,2) = 1/3 * 1/3 * 1/3 = 1/27

P(At least five hours study) = 2/27 + 2/27 + 1/27 = 5/27