Hamza comes to office located in Islamabad through different modes of

Pearl Carney

Pearl Carney

Answered question

2021-12-04

Hamza comes to office located in Islamabad through different modes of transport. From his past data, it is known that the probability of him coming through car, bus, motobrike and rickshaw are respectively 310,15,110 and 25. The probabilities that he will arrive to his office late are 14,13,and 112 if he comes by car, bus and motorbike. Interestingly, he will not be late if he comes by rickshaw. Suppose, he arrives late on Friday. What is the probability that he came by car?

Answer & Explanation

Ida Perry

Ida Perry

Beginner2021-12-05Added 20 answers

Step 1
The provided probabilities are;
P(coming through car) =310
P(coming through bus) =15
P(coming through motorbike) =110
P(coming through rickshaw) =25
P(late by car) =14
P(late by bus) =13
P(late by motorbike) =112
P(late by rickshaw) =0
Step 2
The probability that he came by car and was late is 310×14=340
The probability that he came by bus and was late is 15×13=115
The probability that he came by motorbike and was late is 110×112=1120
The probability that he came by rickshaw and was late is 25×0=0
Therefore, the total probability that he was late is,
P(late)=340+115+1120+0=320
If he was late, the probability that he came by car is 340320=12

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