A coin is tossed three times, where
(i) E : head on 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
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Correct option is
B
0.50,0.42,0.85
If a coin is tossed three times, then the sample space S is
S={HHH,HHT,HTH,HTT,THH,THT,TTH,TTT}
It can be seen that the sample space has 8 elements.
(i) E={HHH,HTH,THH,TTH}
F={HHH,HHT}
∴E∩F={HHH}
P(F)=
8
2
=
4
1
and P(E∩F)=
8
1
P(E∣F)=
P(F)
P(E∩F)
=
4
1
8
1
=
8
4
=
2
1
=0.50
(ii) E={HHH,HHT,HTH,THH}
F={HHT,HTH,HTT,THH,THT,TTH,TTT}
∴E∩F={HHT,HTH,THH}
Clearly, P(E∩F)=
8
3
and P(F)=
8
7
P(E∣F)=
P(F)
P(E∩F)
=
8
7
8
3
=
7
3
=0.42
(iii) E={HHH,HHT,HTT,HTH,THH,THT,TTH}
F={HHT,HTT,HTH,THH,THT,TTH,TTT}
∴E∩F={HHT,HTT,HTH,THH,THT,TTH}
P(F)=
8
7
and P(E∩F)=
8
6
Therefore, P(E∣F)=
P(F)
P(E∩F)
=
8
7
8
6
=
7
6
=0.85
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