Problem 3 A survey about sports revealed that 28 watched gym

Problem 3: A survey about sports revealed that 28% watched gymnastics, 29% watched baseball, 19% watched soccer, 14% watched both gymnastics and baseball, 12% watched baseball and soccer, 10% watched gymnastics and soccer, and 8% watched all three sports. (Hint: Draw a Venn Diagram).

What percent of people watched none of these three sports? (4 points)

If someone watched gymnastics, what is the probability that they did not watch baseball? (5 points)

Solution

A)

Note that

P(watched none) = 1 - P(G U B U S)

As

P(G U B U S) = P(G) + P(B) + P(S) - P(G and B) - P(GB and S) - P(G and S) + P(G and B and S)

= 0.28 + 0.29 + 0.19 - 0.14 - 0.12 - 0.10 + 0.08

= 0.48 [ANSWER]

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B)

P(B\'|G) = P(B\' and G) / P(G)

As

P(B\' and G) = P(G) - P(B and G) = 0.28 - 0.14 = 0.14,

Then

P(B\'|G) = 0.14/0.28 = 0.5 [ANSWER]