Question

Question #a7582

Answer 1

The overall probability of being late `p(L)=0.17`
The probability of not late and commuting by car `=24/83`

Explanation:

(1) Let's calculate the probability of johnny being late

train = T
car = C
bike = B
late =L
not late =`barL`

`p(TnnL)=0.2*0.3=0.06`

`p(CnnL)=0.3*0.2=0.06`

`p(BnnL)=0.5*0.1=0.05`

`p(L)=p(TnnL)+p(CnnL)+p(BnnL)=0.06+0.06+0.05=0.17`

The overall probability of being late `p(L)=0.17`

(2)Probability of Johnny not being late `p(barL)=1-0.17=0.83`

`(p(barL nn C))=0.3*0.8=0.24`

We need to calculate `p_(barL)(C)=(p(barL nn C))/(p(barL))=(0.8*0.3)/0.83=0.24/0.83`