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(\text{monday}) = \\)
\\(p(\text{starts with s}) = \\)
\\(p(\text{monday or starts with s}) = \\)

Explanation:

Identify the sample space and events

Using the Theoretical Probability knowledge point
The sample space \(S\) consists of the 7 days of the week:

$$ S = \{\text{Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday}\} $$

The total number of outcomes is \(n(S) = 7\).

Calculate the probability of choosing Monday

Using the Theoretical Probability knowledge point
Let event \(A\) be choosing Monday:

$$ A = \{\text{Monday}\} \implies n(A) = 1 $$

$$ P(\text{Monday}) = \frac{1}{7} $$

Calculate the probability of choosing a day starting with S

Using the Theoretical Probability knowledge point
Let event \(B\) be choosing a day that starts with the letter S:

$$ B = \{\text{Saturday, Sunday}\} \implies n(B) = 2 $$

$$ P(\text{starts with S}) = \frac{2}{7} $$

Apply the addition rule for mutually exclusive events

Using the Mutually Exclusive Events knowledge point
Since a day cannot be both Monday and start with the letter S, the events are mutually exclusive:

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

Answer:

A day of the week is randomly chosen. What is the probability of choosing Monday or a day that starts with the letter S?
\(P(\text{Monday}) =\) <blank>\(\frac{1}{7}\)</blank>
\(P(\text{starts with S}) =\) <blank>\(\frac{2}{7}\)</blank>
\(P(\text{Monday or starts with S}) =\) <blank>\(\frac{3}{7}\)</blank>