The odds against a certain event p are 7:4 and odds in favour of another event q is independent of p are 8:7 the probability that at least one of the events will happen is
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Let probability of the first event taking place be A and probability of the second event taking place be B.
Then,
P(A)=35+3=3/8P(B)=77+5=7/12
The required event can be defined as that Atakes place and B does not take place (A or Btakes place and A does not take place or Atakes place and B takes place.)
=[P(A){1−P(B)}]+[P(B){1−P(A)}]+[P(A)P(B)]
=[38×512]+[58×712]+[38×712]
=15+35+21/96
=71/96
Then,
P(A)=35+3=3/8P(B)=77+5=7/12
The required event can be defined as that Atakes place and B does not take place (A or Btakes place and A does not take place or Atakes place and B takes place.)
=[P(A){1−P(B)}]+[P(B){1−P(A)}]+[P(A)P(B)]
=[38×512]+[58×712]+[38×712]
=15+35+21/96
=71/96
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