Question S (1 point) A class has 12 students, 8 female and 4 male. Randomly choo

Question

Question S (1 point) A class has 12 students, 8 female and 4 male. Randomly choose 3 students. What is the probability that 1 female and 2 males are chosen? Question 6 (1 point) reverts A and B are independent with P(A)-0.6 and P(B)-03, find P(A or B). Question 7 (I point) If events A and B are independent with P(A)-0.6 and P(B)-0.4, find the probability that neither event A nor event B happens. Question 8 (1 point) Given P(B) 0.3 and P(A B)-0.7, find P(A and B) Question 9 (I point) Given P(B) 0.6, P(A) 0.1, and P(AlB) 0.7, find P(BIA). 21Pag

Explanation / Answer

5)
8 female and 4 male
3 students are chosen
P(1 female and 2 males)
= 8C1 * 4C2 / 12C3
= 8 * 6 /(12 *11 *10/6 )
= 0.21818

6)

when A and B are independent
P(A and B) = P(A) * P(B)
P(A or B)   = P(A) + P(B) - P(A and B)
= 0.6+0.3-0.6*0.3
=0.72

7)
we need to find P((A or B)' ) = 1 - P(A or B)
= 1 - (P(A) + P(B) - P(A and B))
= 1 - (0.6 +0.4 - 0.6*0.4)
= 0.24

P(A|B) = P(A and B) /P(B)

0.7 = P(A and B) /(1- P(B'))

P(A and B) = 0.7* (1 - 0.3)

= 0.49

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