A fair coin tossed 3 times. What is the probability of event Results of the first tossing and of the second tossing coincide?
Answers
Answer:
Given, a fair coin is tossed thrice
∴Total no.of outcomes=2\times 2\times2=8
A: Probability for first toss to be head,P(A)=
8
4
=
2
1
(since no.of outcomes are {HTT,HHH,HHT,HTH})
B: Probability for second toss to be head,P(B)=
8
4
=
2
1
(since no.of outcomes are {THT,HHH,HHT,THH})
C: Probability of two consecutive heads or tails,P(C)=
8
4
=
2
1
(since no.of outcomes are {HTT,THH,HHT,TTH})
Consider,P(A∩B∩C)=
8
1
(since HHT is common events)
P(A)×P(B)×P(C)=
2
1
×
2
1
×
2
1
=
8
1
P(A∩B∩C)=P(A)P(B)P(C)
⇒A,B,Care independent events.
Consider,P(A∩B)=
8
2
=
4
1
(since HHH,HHT are common events)
P(A)×P(B)=
2
1
×
2
1
=
4
1
P(A∩B)=P(A)P(B)
⇒A,Bare independent events.
Consider,P(B∩C)=
8
2
=
4
1
(since THH,HHT
P(C)×P(A)=
2
1
×
2
1
=
4
1
P(C∩A)=P(C)P(A)
⇒C,Aare independent events.
⇒A,B,Care pairwise independent.
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