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) = 0.5^{3}

= **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 - 0.9^{3}

= **0.271**

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