(b) 65 : 23
If the probability of an event is P then the odds against its occurrence are 1 – P to P.
Selecting 1 from the 4 number 1, 2, 3,4, can be done in 4 ways
Here for the event A we are given that = (1 - P)/P = 7/4
⇒ 4 – 4P = 7P
⇒ 11 P = 4 ⇒ P = 4/11 ⇒ P(A) = 4/11 for the event B
We are given
(1 - P)/P = 5/3 ⇒ 5P = 3 – 3P
⇒ 8P = 3 ⇒ P = 3/8
P(B) = 3/8
Now we are given P(A) + P(B) + P(C) = 1
P(C) = 1 – P(A) – P(B)
P(C) = 1 - (4/11) - (3/8)
(i.e.,)