Question

1) The probability of drawing a pink chip from a bowl of different-colored chips is 0.35, theprobability of drawing a blue chip is 0.46, the probability of drawing a green chip is 0.15, and the probability of drawing a purple chip is 0.04. What is the probability that a blue or a purple chip will be drawn?2) If a manufacturer is trying to put together a sample collection of her product and order isnot important, how many combinations can be created with 15 items that will be placed in packages containing five items? If order is important, how many permutations can be created?

Answer 1

Answer:

1) 0.5 or 50%.

2) Order does not matter: 3,003 combinations.

   Order matters: 360,360 permutations.

Step-by-step explanation:

1) The probability of drawing either a purple or a blue chip is the sum of both individual probabilities:

$P(B\ or\ P) = P(B) +P(P) = 0.46+0.04\\P(B\ or\ P) = 0.50$

the probability that a blue or a purple chip will be drawn is 0.5 or 50%.

2)

a) Choose 5 items from a  total of 15 items when order does not matter:

$C(15,5) = \frac{15!}{(15-5)!5!}=\frac{15*14*13*12*11}{5*4*3*2*1}\\C(15,5) = 3,003$

b) Choose 5 items from a  total of 15 items when order matters:

$P(15,5) = \frac{15!}{(15-5)!}=15*14*13*12*11}\\P(15,5) = 360,360$