A doctor is to visit a patient. From the past experience, it is known that the probabilities that he will come by train, bus, scooter or by other means of transport are respectively 310,15,110 and 25. The probabilities that he will be late are 14,13 and 112, if he comes by train, bus and scooter respectively, but if he comes by other means of transport, then he will not be late. When he arrives, he is late. Then the probability that he comes by train is

E1=come by trainE2=come by busE3=come by scooterE4=come by any other means of trans fortPE1=310 PE2=15 PE3=110 PE4=25A=he arrirves but he is latePAE1=14 PAE2=13 PAE3=112 PAE4=0PE1A=310×14310×14+15×13+110×112+25×0 =99+8+1=918=12

A doctor is to visit a patient. From the past experience, it is known that the probabilities that he will come by train, bus, scooter or by other means of transport are respectively 310,15,110 and 25. The probabilities that he will be late are 14,13 and 112, if he comes by train, bus and scooter respectively, but if he comes by other means of transport, then he will not be late. When he arrives, he is late. Then the probability that he comes by train is

E1=come by trainE2=come by busE3=come by scooterE4=come by any other means of trans fortPE1=310 PE2=15 PE3=110 PE4=25A=he arrirves but he is latePAE1=14 PAE2=13 PAE3=112 PAE4=0PE1A=310×14310×14+15×13+110×112+25×0 =99+8+1=918=12

AI Mentor

Check Your IQ

Free Expert Demo

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

A doctor is to visit a patient. From the past experience, it is known that the probabilities that he will come by train, bus, scooter or by other means of transport are respectively $\frac{3}{10}, \frac{1}{5}, \frac{1}{10} a n d \frac{2}{5} .$ The probabilities that he will be late are $\frac{1}{4}, \frac{1}{3} a n d \frac{1}{12},$ if he comes by train, bus and scooter respectively, but if he comes by other means of transport, then he will not be late. When he arrives, he is late. Then the probability that he comes by train is

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

$\frac{3}{5}$

$\frac{2}{3}$

$\frac{1}{2}$

$\frac{1}{3}$

answer is A.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

$E_{1} =$ come by train

$E_{2} =$ come by bus

$E_{3} =$ come by scooter

$E_{4} =$ come by any other means of trans fort

$P (E_{1}) = \frac{3}{10} P (E_{2}) = \frac{1}{5} P (E_{3}) = \frac{1}{10} P (E_{4}) = \frac{2}{5}$

A=he arrirves but he is late

$\begin{array}{rcl} P (\frac{A}{E_{1}}) & = & \frac{1}{4} P (\frac{A}{E_{2}}) = \frac{1}{3} P (\frac{A}{E_{3}}) = \frac{1}{12} P (\frac{A}{E_{4}}) = 0 \\ P (\frac{E_{1}}{A}) & = & \frac{\frac{3}{10} \times \frac{1}{4}}{\frac{3}{10} \times \frac{1}{4} + \frac{1}{5} \times \frac{1}{3} + \frac{1}{10} \times \frac{1}{12} + \frac{2}{5} \times 0} \\ = & \frac{9}{9 + 8 + 1} = \frac{9}{18} = \frac{1}{2} \end{array}$