Question

If a and b are two mutually exclusive and exhaustive events with p(b) = 3p(a), then what is the value of ?

Answer 1

ANSWER:

⇒  Mutually Exclusive Events: Two events A & B of a single experiment are said to be Mutually Exclusive or Disjoint Events if and only if they cannot both occur at the same time.

Example: In the coin-tossing experiment, we cannot get Head & Tail at the same time.

⇒ Exhaustive Events: Events are said to be Exhaustive when the union of mutually exclusive events is equal to entire sample space.

Example: In the coin-tossing experiment, Head & Tail are collectively Exhaustive Events.

EXAMPLE:

S={1,2,3,4,6,8,10,12}       ; n(S)= 8

⇒ Let "a" be the event of getting Odd numbers

a={1,3}                             ; n(a)= 2    &

P(a) = 2/8 = 1/4

P(a) =  1/4

⇒ Let "b" be the event of getting Even numbers

b={2,4,6,8,10,12}             ; n(b)= 6

Pb) = 6/8 = 3/4

P(b) =  3/4

Now in this example

• both a and b are two mutually exclusive and exhaustive events AND
• p(b) = 3 p(a)

So you can find Your desired value.