Consider the probability experiment of flipping a fair coin four times in a row.

Question

Consider the probability experiment of flipping a fair coin four times in a row. (a) What is its sample space? (b) Find P(A) where A is the event that heads are not flipped twice in a row; that is, whenever heads are flipped, the very next flip (if there is one) is not heads. (c) Find P(B) where B is the event that exactly two tails are flipped; that is, precisely two of the four flips are tails, forcing the remaining two to both be heads. (d) Find P(A and B). (e) Find P(A or B). (f) Find P(A|B).

Explanation / Answer

Answer:

a). sample space

{HHHH,HHHT,HHTH,HHTT,HTHH,HTHT,HTTH,HTTT,THHH,THHT,THTH,THTT,TTHH,TTHT,TTTH,TTTT}

b).

A={HTHT,HTTH,HTTT,THTH,THTT,TTHT,TTTH,TTTT}

number of favorable outcomes=8

P=8/16 =0.5

c).

B={ HHTT ,HTHT,HTTH ,THHT,THTH,TTHH}

P=6/16 =0.375

d).

P( a and B) = 3/16

=0.1875

e). (8+6-3)/16 =11/16

=0.6875

f). P( A/B) = P( A and B)/P(B) =0.1875/0.375

=0.5

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