Question

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?

Answer 1

Answer:

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