Question

Q1. Determine P: A coin is tossed three times.
(i) E: heads on the third toss, F: heads on first two tosses.
(ii) E: at least two heads, F: at most two heads.
(iii) E: at most two tails, F: at least one tail.

Answer 1

Answer:

1/2

3/7

6/7

Step-by-step explanation:

Total Cases

H   H    H

H   H   T

H   T    H

H   T    T

T   H   H

T   H   T

T   T   H

T   T   T

E :head on third toss

P(E)  = 4/8  = 1/2

heads on first two tosses

P(F) = 2/8 = 1/4

E ∩ F = {H   H    H}

P ( E ∩ F) = 1/8

P(E|F) = P ( E ∩ F)/ P(F)   =  (1/8)/(1/4)  = 1/2

E : at least two heads ,

P(E) = 4/8  = 1/2

F : at most two heads

= 1 -  3 Heads

P(F) = 1  - 1/8  = 7/8

E ∩ F = Two Heads = 3/8

P(E|F) =  (3/8) / (7/8)  = 3/7

(iii) E : at most two tails ,

p(E) = 1 - 3 Tails = 1 - 1/8  = 7/8

F : at least one tail

P(F) = 1 - No Tail = 1  - 1/8  = 7/8

E ∩ F = 1 - No Tail - All Tails  = 1 - 2/8  = 3/4

P(E|F) =  (3/4)/(7/8)

= 6/7