Question

in a class of 151 students, 97 are taking math (m), 78 are taking science (s), and 55 are taking both math and science. one student is picked at random.
find the probability
p(taking math or science or both)
p(taking math or science or both) = \square
(round to three decimal places as needed)

Explanation:

Step1: Apply addition rule for sets

$n(M \cup S) = n(M) + n(S) - n(M \cap S)$

Step2: Substitute given values

$n(M \cup S) = 97 + 78 - 55 = 120$

Step3: Calculate probability

$P(M \cup S) = \frac{n(M \cup S)}{n(\text{Total students})} = \frac{120}{151}$

Step4: Round to 3 decimal places

$\frac{120}{151} \approx 0.795$

Answer:

0.795