Question

8. Colleen times her morning commute such that there is an equal likelihood that she will arrive early or late to work on any given day. If she always arrives either early or late, what is the probability that Colleen will arrive late to work no more than twice during a five-day workweek

Answer 1

Solution :

Case I :

If Collen is late on $0$ out of $5$ days.

$= \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2}$

$=\frac{1}{32}$

Case II :

When Collen is late on $1$ out of $5$ days.

$= \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times ^5C_1$

$=\frac{1}{32} \times 5$

$=\frac{5}{32}$

Case III :

When Collen was late on $2$ out of $5$ days.

$= \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times ^5C_2$

$=\frac{1}{32} \times 10$

$=\frac{5}{16}$

Therefore, the $\text{probability}$ that Collen will arrive late to work no more than $\text{twice}$ during a $\text{five day workweek}$ is :

$=\frac{1}{32} + \frac{5}{32} + \frac{5}{16}$

$=\frac{1}{2}$