Solution
Back-up Theory
If X = number of heads obtained when 5 fair coins are flipped, then
P(X = x) = (5Cx)(½)5 = (5Cx)/32
Now to work out the solution,
1. p(E) = {(5C0) + (5C2) + (5C4)}/32 [note that 0 is an even number]
= ½ Answer 1
2. p(F) = {(5C4) + (5C5)}/32
= 6/32 Answer 2
3. p(G) = (5C5)/32
= 1/32 Answer 3
4. p(H) = ½ Answer 4
5. p(E/H) = P(E and H)/P(H)
= [{(4C1) + (4C3)}/32]/(1/2)
= ½ Answer 5
6. p(F/H) = P(F and H)/P(H)
= [{(4C3) + (4C4}/32]/(1/2)
= 5/16 Answer 6
7. p(E/F) = P(E and F)/P(F)
= [{(5C4)}/32]/(6/32)
= 5/6 Answer 7
8. p(G/H) = P(G and H)/P(H)
= [{(4C4)}/32]/(1/2)
= 1/16 Answer 8
9. Since p(E/H) = ½ = P(E), E and H are independent. Answer 9
p(E and F) = 5/32 [vide (7)]; p(E) x p(F) = 3/32 [vide (1) and (2)]
Since p(E and F) is not equal to p(E) x p(F), E and F are not independent. Answer 10
p(F and H) = ¼ [vide (6)]; p(F) x p(H) = 3/32 [vide (2) and (4)]
Since p(F and H) is not equal to p(F) x p(H), F and H are not independent. Answer 11
10. p(G and H) = 1/32 [vide (8)]; p(G) x p(H) = 1/64 [vide (3) and (4)]
Since p(G and H) is not equal to p(G) x p(H), F and H are not independent. Answer 12
DONE
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