Question

24. WORK SCHEDULE You work 3 evenings each week at a bookstore. Yoursupervisor assigns you 3 evenings at random from the 7 possibilities. Whatis the probability that your schedule this week includes working on Friday

Answer 1

P(that his schedule this week incldes working on friday) = 1/35

Step-by-step explanation:

You work 3 evenings each week

Step1: find the total outcomes

`\begin{gathered} \text{The total outcomes can be calculated by using combination} \\ ^nC_{^{}r}\text{ = }\frac{n!}{(n\text{ - r)!r!}} \\ \text{n = 7 and r = 3} \\ ^7C_3\text{ = }\frac{7!}{(7\text{ - 3)!3!}} \\ ^7C_3\text{ = }(7!)/(4!3!) \\ ^7C_3\text{ = }\frac{7\text{ x 6 x 5 x 4 x 3 x 2 x 1}}{4\text{ x 3 x 2 x1! 3 x 2 x 1}} \\ ^7C_3\text{ = }\frac{7\text{ x 6 x 5}}{3\text{ x 2 x1}} \\ ^7C_3\text{ = }(210)/(6) \\ ^7C_3\text{ = 35} \\ \text{Therefore, the total possible outcomes is 35} \end{gathered}`

Probability that his schedule will include friday is

Possible outcome of including a friday is 1

Probability of including a friday = 1 / 35

Therefore, the probability of including a friday is 1/35