Question

a day of the week is randomly chosen. what is the probability of choosing monday or a day that starts with the letter s? p(monday) = p(starts with s) = p(monday or starts with s) = 2/7 3/7 5/7

Explanation:

Step1: Calculate P(Monday)

There are 7 days in a week and Monday is 1 day. So $P(\text{Monday})=\frac{1}{7}$.

Step2: Calculate P(starts with S)

The days that start with S are Saturday and Sunday, 2 days out of 7. So $P(\text{starts with }S)=\frac{2}{7}$.

Step3: Calculate P(Monday or starts with S)

Since Monday is not a day that starts with S, we use the addition - rule for mutually - exclusive events $P(A\cup B)=P(A)+P(B)$. Here $A$ is the event of choosing Monday and $B$ is the event of choosing a day that starts with S. So $P(\text{Monday or starts with }S)=\frac{1 + 2}{7}=\frac{3}{7}$.

Answer:

$P(\text{Monday})=\frac{1}{7}$
$P(\text{starts with }S)=\frac{2}{7}$
$P(\text{Monday or starts with }S)=\frac{3}{7}$