Question

Out of a group of 120 students that were surveyed about water sports, 28 said they ski and 52 said they wake

board. 16 of the students who said they ski said they also wake board. If a student is chosen at random, find
P( skiſ does not wake board)

Answer 1

The probability that a randomly chosen student skis but does not wakeboard is 0.10, indicating a 10% chance for this event to occur.

Step-by-step explanation:

To calculate the probability that a student chosen at random skis but does not wakeboard, we need to find the number of students who only ski. According to the question, 28 students ski, and 16 of those also wakeboard. To find those who only ski, we subtract the number of students who do both from the total number of skiers: 28 (total skiers) - 16 (those who also wakeboard) = 12 students who only ski.

The probability that a randomly chosen student skis but does not wakeboard is thus the number of students who only ski divided by the total number of students surveyed. We calculate it as follows: P(Ski ∉ does not wakeboard) = 12 students who only ski / 120 total students surveyed = 0.10.

The final answer is 0.10, which means there is a 10% chance that a student selected at random skis but does not wakeboard.

Answer 2

10% of the students ski and do not wake board

Step-by-step explanation:

The total number of students is 120. 28 students ski while 52 students wake board. 16 of the students ski and wake board.

Let S represent students who ski and W represent those who wake board also W' represent those who do not wake board.

Therefore:

S = 28

W = 52

n = total number of student = 120

S ∩ W = those who ski and wake board = 16

Those who ski and do not wake board = S ∩ W' = S - (S ∩ W) = 28 - 16 = 12

Probability of those who ski and do not wake board = (S ∩ W') / n = 12 / 120 = 0.1 = 10%

10% of the students ski and do not wake board