Please help solve these problems step by step so I could learn the routine myself. Thank you!   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: Find the probability that a hiker likes Gatorade or energy bars If a hiker likes Gatorade, find the probability that he likes energy bars If a hiker likes energy bars, find the probability that he likes Gatorade.

A First Course in Probability (10th Edition)
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Please help solve these problems step by step so I could learn the routine myself. Thank you!

 

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:

  1. Find the probability that a hiker likes Gatorade or energy bars
  2. If a hiker likes Gatorade, find the probability that he likes energy bars
  3. If a hiker likes energy bars, find the probability that he likes Gatorade.
Expert Solution
Step 1

Given:

Probability for the G (Gatorade) and E (Energy)

PG=0.50PE=0.40PGE=0.20

 

 

Step 2

2.

PGE=PG+PE-PGE=0.50+0.40-0.20=0.70

70% probability that the researcher likes Gatorade or energy bars.

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