Ivan's favorite colors are / blue{/text{blue}}blue and / green{/text{green}}green. He has / blue{/text{1 blue shirt}}1 blue shirt, / green{/text{1 green shirt}}1 green shirt, / blue{/text{1 blue hat}}1 blue hat, / green{/text{1 green belt}}1 green belt, / blue{/text{1 blue pair of pants}}1 blue pair of pants, and / green{/text{1 green pair of pants}}1 green pair of pants. Ivan selects one of these garments at random. Let A be the event that he selects a green garment and B be the event that he chooses a pair of pants. What is P (A/text{ or }B) P (A or B), the probability that the garment Ivan chooses is either green or a pair of pants?

Question

Mathematics

Molly Good

4 August, 11:34

Ivan's favorite colors are / blue{/text{blue}}blue and / green{/text{green}}green. He has / blue{/text{1 blue shirt}}1 blue shirt, / green{/text{1 green shirt}}1 green shirt, / blue{/text{1 blue hat}}1 blue hat, / green{/text{1 green belt}}1 green belt, / blue{/text{1 blue pair of pants}}1 blue pair of pants, and / green{/text{1 green pair of pants}}1 green pair of pants. Ivan selects one of these garments at random. Let A be the event that he selects a green garment and B be the event that he chooses a pair of pants. What is P (A/text{ or }B) P (A or B), the probability that the garment Ivan chooses is either green or a pair of pants?

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Answers (1)

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Zaid Cantu · Answer 1

P (A or B) = 2/3

Step-by-step explanation:

Blue Garments = 1 blue shirt, 1 blue hat, 1 blue pair of pants

Total blue garments = 3

Green garments = 1 green shirt, 1 green hat, 1 green pair of pants

Total green garments = 3

Total no. of garments = blue garments + green garments = 6

A = event that Ivan selects a green garment

P (A) = Favourable outcomes/Total no. of outcomes

P (A) = 3/6

B = event that Ivan chooses a pair of pants

P (B) = 2/6

We need to find P (A or B) = P (A∪B)

By formula, P (A∪B) = P (A) + P (B) - P (A∩B)

P (A∩B) = Probability that a green pair of pant is chosen = 1/6

P (A∪B) = 3/6+2/6-1/6

= 4/6

=2/3