Question

select the correct answer.
at michael’s school, 38% of the students have a pet dog and 24% of the students have a pet cat. michael found that 11% of the students had both a pet dog and a pet cat.
what is the probability that a randomly chosen student at michael’s school will have a pet dog or a pet cat?
a. 83%
b. 62%
c. 40%
d. 51%

Explanation:

Step1: Recall addition rule

For events $A$ (have dog) and $B$ (have cat):
$$P(A \cup B) = P(A) + P(B) - P(A \cap B)$$

Step2: Substitute given values

$P(A)=38\%$, $P(B)=24\%$, $P(A \cap B)=11\%$
$$P(A \cup B) = 38\% + 24\% - 11\%$$

Step3: Calculate the result

$$P(A \cup B) = 51\%$$

Answer:

D. 51%