Question

For a certain​ candy, 20​% of the pieces are​ yellow, 5​% are​ red, 15​% are​ blue, 10​% are​ green, and the rest are brown. ​

a) If you pick a piece at​ random, what is the probability that it is​ brown? it is yellow or​ blue? it is not​ green? it is​ striped? ​

b) Assume you have an infinite supply of these candy pieces from which to draw. If you pick three pieces in a​ row, what is the probability that they are all​ brown? the third one is the first one that is​ red? none are​ yellow? at least one is​ green?

Answer 1

a) P(yellow) = 0.2

P(red) = 0.05

P(blue) = 0.15

P(green) = 0.1

P(brown) = 1 - (0.2+0.05+0.15+0.1)

= 0.5

P(yellow or blue) = 0.2+0.15

= 0.35

P(not green) = 1 - P(green)

= 1 - 0.1

= 0.9

P(stripped) = 0

b) P(all three are brown) = 0.5³

= 0.125

P(third one is the first one that is​ red) = P(first 2 are not red) x P(red)

= (1 - 0.05)² x 0.05

= 0.045

P(none are yellow) = (1 - P(yellow))³

= (1 - 0.2)³

= 0.512

P(at least one green) = 1 - P(none are green)

= 1 - 0.9³

= 0.271