The odds that a book will be favourably reviewed by three independent critics are 5 to 2, 4 to 3, and 3 to 4 respectively; what is the probability that of the three reviews a majority will be favourable?
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2
P
1
,P
2
&P
3
be probability of favorable review
P
1
=
7
5
P
3
=
7
3
P
1
1
=
7
2
P
3
1
=
7
4
P
2
=
7
4
P
2
1
=
7
3
For majority at least two must be favorable
Required probability=
7
5
×
7
3
×
7
4
+
7
2
×
7
4
×
7
3
+
7
5
×
7
3
×
7
4
+
7
5
×
7
4
×
7
3
=
7
3
60
+
7
3
24
+
7
3
60
+
7
3
60
=
343
204
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