Question

applying the addition rule of mutually exclusive events
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: Use addition rule for mutually - exclusive events

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

Answer:

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