Question

the table below gives the probability density of trees in a particular park. if a tree is selected at random, what is the probability that it is a birch or walnut? p = ?

Explanation:

Step1: Identify the probabilities

The probability of a birch tree \( P(\text{Birch}) = 0.19 \), and the probability of a walnut tree \( P(\text{Walnut}) = 0.26 \).

Step2: Use the addition rule for mutually - exclusive events

Since a tree cannot be both a birch and a walnut at the same time (mutually - exclusive events), the formula \( P(A\cup B)=P(A)+P(B) \) is used. Here \( A \) is the event of selecting a birch tree and \( B \) is the event of selecting a walnut tree.
So \( P(\text{Birch}\cup\text{Walnut})=P(\text{Birch}) + P(\text{Walnut}) \).
Substitute the values: \( P(\text{Birch}\cup\text{Walnut})=0.19 + 0.26 \).

Step3: Calculate the sum

\( 0.19+0.26=\frac{19 + 26}{100}=\frac{45}{100}=0.45 \).

Answer:

\( 0.45 \)