EXAMPLE 3.4.9

Refer to the data on scholarships in the table presented earlier (see EXAMPLE 3.6.9)

1. What is the probability that a randomly-chosen student received a full scholarship, given that he/she received some sort of scholarship?

Since the information is given in terms of percents, we will pretend that the total population is 100.

Since 38 received some sort of scholarship, and 6 of those 38 received a full scholarship,

P(full scholarship, given some sort of scholarship) = 6/38 or roughly .158.

2. What is the probability that a randomly chosen student received a scholarship, given that he/she had a score less than 501?

Since 74 had scores less than 501, and 12 of those 74 received a scholarship,

P(scholarship, given score < 501) = 12/74 or roughly .16.