Question

Let E and F be any two events with P(EUF) = 0.8, P(E) = 0.4 and P(E/F) = 0.3. Then P(F) is
1. 3/7
2. 4/7
3. 3/5
4. 2/5

Answer 1

Correct Answer - Option 2 : 4/7

Concept:

P(E/F) = \(\frac{{{\rm{P}}\left( {{\rm{E}} ∩ {\rm{F}}} \right)}}{{{\rm{P}}\left( {\rm{F}} \right)}}\)

P(E⋂F) = P(E/F) × P(F)

P(E⋂F) = 0.3 P(F)                ---(1)

Also, P(EUF) = P(E) + P(F) - P(E⋂F)

0.8 = 0.4 + P(F) - 0.3 P(F)                (From equation (i))

0.4 = 0.7 P(F)

P(F) = \(\frac{4}{7}\)