Test each pair of events for independence 1) A and D 2) A and E 3) B and D 4) B and E 5) B and F 6) C and F 7) A and B 8) D and F

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by sweetysiri92

2015-03-24T13:16:12+05:30

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The pair of events that are independent are:

2.) A and E.
P(AΠE) = 0.28
P(A)*P(E) = 0.7*0.4 = 0.28
Hence, A and E are independent.

3.) B and D.
P(BΠD)= 0.03
P(B)*P(D)= 0.1*0.3 = 0.03
Hence, A and E are independent.

6.) C and F.
P(CΠF)= 0.06
P(C)*P(F)= 0.2*0.3 = 0.06
Hence, A and E are independent.

But, 1,4,5,7 and 8 do not comply to this condition hence they are not independent.

Hope i helped u:)
2015-03-24T15:25:14+05:30

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
Two arbitrary events A and B are said to be independent if any one of the following three equivalent conditions hold:
1. P(A ∩ B) = P(A)P(B)
2. P(A|B) = P(A) - B has no effect on A
3. P(B|A) = P(B) - A has no effect on B

2 and 3 are calculated after calculating 1. So check condition 1. If it satisfies, then they are independent, otherwise they aren't.

1) A and D
P(A ∩ D) = 0.2
P(A)P(D) = 0.7 x 0.3 = 0.21
So A and D are not independent.

2) A and E
P(A ∩ E) = 0.28
P(A)P(E) = 0.7 x 0.4 = 0.28
So A and E are independent.

3) B and D
P(B ∩ D) = 0.03
P(B)P(D) = 0.1 x 0.3 = 0.03
So B and D are independent.

4) B and E
P(B ∩ E) = 0.05
P(B)P(E) = 0.1 x 0.4 = 0.04
So B and E are not independent.

5) B and F
P(B ∩ F) = 0.02
P(B)P(F) = 0.1 x 0.3 = 0.03
So B and F are not independent.

6) C and F
P(C ∩ F) = 0.06
P(C)P(F) = 0.2 x 0.3 = 0.06
So C and F are independent.

7) A and B
P(A ∩ B) = 0 (Since they are mutually exclusive)
P(A)P(B) = 0.7 x 0.1 = 0.07
So A and B are not independent.

8) D and F
P(D ∩ F) = 0 (Since they are mutually exclusive)
P(D)P(F) = 0.3 x 0.3 = 0.09
So D and F are not independent.