Question

Red

Orange

Yellow

Green

Purple

Total

1046.

1066

977

1029

969

5087

Suppose you are going to randomly select two Skittles from the bag YOU purchased.

• (a) What is the probability that both Skittles are purple if you select them with replacement? Give your answer correct to four decimal places. (4 points)
• (b) What is the probability that both Skittles are purple if you select them without replacement? Give your answer correct to four decimal places. (4 points)
• (c) What is the probability that the first skittle is purple and the second skittle is not purple if you select them with replacement? (4 points)
• (d) What is the probability that at least one Skittle is purple if you select them with replacement? (4 points)

*show your work

Answer 1

Part a

When first is purple probability is 969/5087

And when you replace it and again choose then having a purple is same as 969/5087

So probability is (969/5087)(969/5087)

= 0.03628

part b)

When first is purple and without replacement 1 is already taken so left with 5086 left and out of 969 purples 968 left..

So (969/5087)(968/5086) = 0.03625

Part c)

First is purple i.e. 969/5087

And after replacing non purples are 4118 out of 5087

So probability is (969/5087)(4118/5087)

= 0.154200

Part D)

Probability that at least one is purple...

So it is equal to 1- probability of no purple

i.e. 1-(4118/5087)

= 0.190485