a) Compute the indicated quant
a) Compute the indicated quantity.
P(A | B) = .1, P(B) = .4. Find P(A ∩ B).
P(A ∩ B) =
b)Compute the indicated quantity.
P(A) = .1, P(B) = .2. A and B are independent. Find P(A ∩B).
P(A ∩ B) =
c)Find the conditional probability of the indicated event whentwo fair dice (one red and one green) are rolled. HINT [See Example1.]
The red one is 1, given that the sum is 7.
Answer:
a) P(A ∩ B) = P(A | B) * P(B) = 0.1 *0.4 = 0.04
b) P(A ∩ B) = P(A) * P(B) = 0.1 * 0.2= 0.02
c) Sample space for sum of 7 = {(1,6), (2,5), (3,4), (4,3),(5,2), (6,1)}
sample space for red one is 7 and sum of 7 = {(1,6)}
P(the red one is 1, given that the sum is 7) = P(the red one is1 and the sum is 7) / P(sum of 7)
= (1/36) / (6/36)
= 1/6
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