Question

A sports survey taken at THS shows that 48% of the respondents liked soccer, 66% liked basketball and 38% liked hockey. Also,30% liked soccer and basketball, 22% liked basketball and hockey, 28% liked soccer and hockey. finally, 12% liked all three sports. A. Draw a. venn diagram to represent the given information. B. What is the probability that a randomly selected student likes basketball or hockey? Solve this by also using an appropriate formula. C. What is the probability that a randomly selected student does not like any of these sports?

Answer 1

a) The Venn diagram is presented in the attached image to this answer.

b) 0.82

c) 0.16

Explanation:

a) The Venn diagram is presented in the attached image to this answer.

n(U) = 100%

n(S) = 48%

n(B) = 66%

n(H) = 38%

n(S n B) = 30%

n(B n H) = 22%

n(S n H) = 28%

n(S n B n H) = 12%

The specific breakdowns for each subgroup is calculated on the Venn diagram attached.

b) The probability that a randomly selected student likes basketball or hockey.

P(B U H)

From the Venn diagram,

n(B U H) = n(S' n B n H') + n(S' n B n H) + n(S n B n H') + n(S n B n H) + n(S n B' n H) + n(S' n B' n H) = 26 + 10 + 18 + 12 + 16 + 0 = 82%

P(B U H) = 82/100 = 0.82

c) The probability that a randomly selected student does not like any of these sports.

P(S' n B' n H')

n(S' n B' n H') = n(U) - [n(S' n B n H') + n(S' n B n H) + n(S n B n H') + n(S n B n H) + n(S n B' n H) + n(S' n B' n H) + n(S n B' n H')]

n(S' n B' n H') = 100 - (26 + 10 + 18 + 12 + 16 + 0 + 2) = 100 - 84 = 16%

P(S' n B' n H') = 16/100 = 0.16