You have two flowers, a yellow one and a red one. The probability that each one

Question

You have two flowers, a yellow one and a red one. The probability that each one is pollinated during its two week blooming period is 0.54. The probability that the red one is pollinated given that the yellow one is pollinated is 0.62.

a) What is the probability that both flowers are pollinated? Give your answer to 2 digits.

b) What is the probability that one or the other or both is pollinated? Give your answer to 2 digits.

c) What is the probability that the yellow flower is pollinated given that the red one is? Give your answer to 2 digits.

d) What is the probability that the yellow flower is pollinated and the red flower is not pollinated? Give your answer to 2 digits

Explanation / Answer

Solution :-

Given,

P(R) = P(Y) = 0.54

P(R|Y) = 0.62

a) P(both flowers are pollinated) = P(R Y) = P(R) * P(Y) = 0.54 * 0.54 = 0.29

b) P(one or the other or both are pollinated) = P(RY)=P(R) + P(Y) P(RY)

= 0.54 + 0.54 - 0.29 = 0.83

c) P(yellow flower is pollinated given that the red one is) = P(Y|R) = P(R|Y) P(Y) / P(R)

= P(Y|R) = 0.62 * 0.54 / 0.54

= 0.62

d) P(yellow is pollinated and red is not pollinated) = P(Y) * (1 - P(R))

= 0.54 * (1 - 0.54)

= 0.54 * 0.46

= 0.25

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