Algebra

Probability

Easy

A doctor is to visit a patient. From the past experiences, it is known that the probabilities of his coming by cab, metro, bike or by other means of transport are respectively 0.3, 0.2, 0.1 and 0.4 respectively. The probabilities that he will be late are 0.25, 0.3, 0.35 and 0.1 if he comes by cab, metro, bike and by other means of transport respectively. using this information about the doctor, answer the following questions :

When the doctor arrives late, what is the probability that he comes by metro?

$\frac{5}{4}$

$\frac{2}{7}$

$\frac{5}{21}$

$\frac{1}{6}$

✅ Correct Option: 2

Total probability of arriving late:

$P(L) = 0.3(0.25) + 0.2(0.3) + 0.1(0.35) + 0.4(0.1) = 0.075 + 0.06 + 0.035 + 0.04 = 0.21$ .

By Bayes' theorem:

$P(\text{metro}|L) = \frac{0.2 \times 0.3}{0.21} = \frac{0.06}{0.21} = \frac{6}{21} = \frac{2}{7}$ .

Question 47

When the doctor arrives late, what is the probability that he comes by cab?

Question 48

When the doctor arrives late, what is the probability that he comes by bike?

Question 49

When the doctor arrives late, what is the probability that he comes by other means of transport?

Question 50

What is the probability that the doctor arrives late ?

When the doctor arrives late, what is the probability that he comes by metro?

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)