three dice were thrown on a table with a basket of 5 red apples and 7 green apples. if two apples are selected one by one without replacement. Find the probability that the first is red and second is green, and the rolled dice would produce at least one 3.
Answers
Given : three dice were thrown on a table with a basket of 5 red apples and 7 green apples
To find : the probability that the first is red and second is green, and the rolled dice would produce at least one 3.
Solution:
basket of 5 red apples and 7 green apples
probability that the first is red and second is green = (5/12)(7/11)
= 35/132
rolled dice would produce at least one 3.
probability of three p = 1/6
probability of not three = 1 - 1/6 = 5/6
probability of atleast 1 three = 1 - probability of 0 three
= 1 - ³C₀p⁰q³
= 1 - (5/6)³
= ( 216 - 125)/216
= 91/216
the probability that the first is red and second is green, and the rolled dice would produce at least one 3. = (35/132) (91/216)
= 3185/28512
= 0.11
Probability = 3185/28512 = 0.11
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