a To calculate the desired probability, we will divide the number of students that were able to memorize the index cards by the total number of students that were tested.
P(able to memorize)= 12/60=1/5
b To determine the probability of a music listener being able to memorize the index card, we should only consider the students listening to music. In total, there were 3+36=45 students that listened to music. Of these, 3 memorized the card. Now we can calculate the probability of a music listener being able to memorize the cards.
P(memorized|loud music)= 3/36=1/12
c If the ability to memorize is unaffected by music, the probability of the students who listened to music and could memorized the card should be the same as the probability of the entire group of students who were tested and could memorize the card.
P(memorized) &=1/5
P(memorized|loud music) &=1/12
The first probability we found in Part A, the latter in Part B. Since the probabilities are not the same, loud music does affect learning ability.
