Question

Sarah 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 Sarah will arrive late to work no more than twice during a five day workweek?

Answer 1

Answer: 0.5

Step-by-step explanation:

Binomial distribution

$P(x)=^nC_xp^x(1-p)^{n-x}$, where P(x) is the probability of getting success inn x trials , n is the number of trails and  p is the probability of getting success in each trial.

Given : Sarah times her morning commute such that there is an equal likelihood that she will arrive early or late to work on any given day.

Then , the probability that Sarah is late on particular day = $\dfrac{1}{2}=0.50$

Then ,  the probability that Sarah will arrive late to work no more than twice during a five day workweek :-

$P(x\leq2)=P(0)+P(1)+P(2)\\\\^5C_0(0.5)^0(0.5)^{5}+^5C_1(0.5)^1(0.5)^{4}+^5C_2(0.5)^2(0.5)^{3}\\\\=(0.5)^5(1+5+\dfrac{5!}{2!3!})=(0.5)^5(16)=0.5$

Hence, the required probability : 0.5