Answer:
The answers to the question are
(a) 1/4
(b) 7/16
(c) 1/16
Step-by-step explanation:
To solve the question we note that
Total number of outcomes = 32
Probability of the event of first three flips are the same =P(F)
Probability of the event of last three flips are the same =P(L)
Total number of outcomes = 2⁵ = 32
The number of ways in which the frist three flips are the same is
F TTTTT, TTTTH, TTTHH, HHHTT, HHHHT, HHHHH, TTTHT, HHHTH = 8
L: TTTTT, HHTTT, HTTTT, THTTT, HHHHH, TTHHH, HTHHH, THHHH = 8
The probability that the first and the last three flips are the same that is
F ∩ L; TTTTT, HHHHH = 2
Therefore P(F ∩ L) = 2/32
(a) P(F) = 8/32 =1/4 also
P(L) = 8/32 =1/4
(b) P(LUF) = P(L) + P(F) - P(F ∩ L) = 1/4+1/4-1/16 =7/16
(c) Let the event of at least two heads among the first three flips be H
and the event of at least two tails among the last three flips be T
Then we have
H; HHHHH, HHHHT, HHHTT, HHHTH, HHTTT, HHTHH, THHTT, THHHT
= 8
T; TTTTT. HTTTT, HHTTT, THTTT, THHTT, HHHTT, THHTT, HTTTH =8
Also H∩T = TTTHH, HHTTT = 2
Therefore P(H ∩ T) = 2/32 = 1/16
