On a rainy day a group of 100 students went to the museum. 60 students brought a

Question

On a rainy day a group of 100 students went to the museum. 60 students brought an umbrella, 50 students brought a backpack and 20 brought neither. If one of them was randomly chosen, find the probability that he or she brought only a backpack with no umbrella and both a backpack and an umbrella On a rainy day a group of 100 students went to the museum. 60 students brought an umbrella, 50 students brought a backpack and 20 brought neither. If one of them was randomly chosen, find the probability that he or she brought only a backpack with no umbrella and both a backpack and an umbrella

Explanation / Answer

P(umbrella) = 60/100 = 0.6

P(backpack) = 50/100 = 0.5

P(no umbrella or backpack) = 20/100 = 0.2

P(umbrella and backpack) = P(umbrella) + P(backpack) - P(umbrella or backpack) = 0.6 + 0.5 - 0.8 = 0.3

A) P(backpack and no umbrella) = P(backpack) - P(backpack and umbrella) = 0.5 - 0.3 = 0.2

B) P(both backpack and umbrella) = 0.3

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