According to a survey of hikers on a trail, 50% of the hikers like Gatorade (G) and 40% like energy bars (E). 20% like both. Assume random selection: a. Find the probability that a hiker likes Gatorade or energy bars b. If a hiker likes Gatorade, find the probability that he likes energy bars c. If a hiker likes energy bars, find the probability that he likes Gatorade.

Explanation:

As per given data

Probability hikers like Gatorade (G) = P(G) = 50% = 0.5

Probability hikers like energy bars = P(E) = 40% = 0.4

Probability hikers like both = P(G and E) = 20% = 0.2

a)

To find the probability that a hiker likes Gatorade or energy bars use the following formula

P(G or E) = P(G) + P(E) - P(G and E )

P(G or E) = 0.5 + 0.4 - 0.2

P(G or E) = 0.7

b)

To find the probability that a hiker likes Gatorade or energy bars use the following formula

P(E|G) = P(E and G)/P(G)

P(E|G) = 0.2/0.5

P(E|G) = 0.4

c)

The probability that he likes Gatorade.

P(G|E) = P(G and E) / P(E)

P(G|E) = 0.2 / 0.4

P(G|E) = 0.5

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