In a class of 154 ​students, 98 are taking math​ (M), 78 are taking science​ (S), and 54 are taking both math and science. One student is picked at random. Find the probability.

Question

In a class of 154 ​students, 98 are taking math​ (M), 78 are taking science​ (S), and 54 are taking both math and science. One student is picked at random. Find the probability. ​P(taking math or science or​ both)

Answer 1

98+78= 176

176 - 54 = 122

122/154 = 61/77 in lowest denominator

Answer 2

The Venn diagram pretty much lays it out for you. The probability of a randomly selected student taking either or both of the subjects is 44 + 54 + 24 = 122. As there are 154 total students, the probability is 122/154, or 79.2%.

Alternatively, 32 are not taking any of those subjects. That's 20.8%. So the complement of that (79.2%) are taking one or both subjects.