A man takes the contract of construction work. The probability is 0.30, if there will be no strike. The probability that the construct work will be completed on time are 0.8 and 0.3 in cases of no strike and in case strike respectively. Find the probability that the construction work will be completed in time.

Options

A. `0.34`
B. `0.56`
C. `0.64`
D. `0.45`

Answer

D

Explanation

Let `E=` event that there is no strike.
`impliesE'=` event that there is strike.
Now `P(E)=0.30`
`impliesP(E')=1-P(E)`
`=1-0.30`
`=0.70`
Let `A=` event that the work completed in time.
`:.P(A//E)=0.8` and `P(A//E')0.3`
`:.P(A)=P(E).P(A//E)+P(E')+P(E').P(A//E')`
`=0.30xx0.8+0.70xx0.3`
`=0.24+0.21`
`=0.45`