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.

Given PE1=310, PE2=15 PE3=110, PE4=25 L-Late PLE1=14, PLE2=13, PLE3=112,PLE4=0WE have to find PE1LBy Bayes theorem PE1L=PE1PLE1PE1PLE1+PE2PLE2+PE3PLE3+PE4PLE4 =310.14310.14+15.13+110.112+25.0=340340+115+1120=3409+8+1120=340×12018=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.

Given PE1=310, PE2=15 PE3=110, PE4=25 L-Late PLE1=14, PLE2=13, PLE3=112,PLE4=0WE have to find PE1LBy Bayes theorem PE1L=PE1PLE1PE1PLE1+PE2PLE2+PE3PLE3+PE4PLE4 =310.14310.14+15.13+110.112+25.0=340340+115+1120=3409+8+1120=340×12018=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 $\frac{3}{10}, \frac{1}{5}, \frac{1}{10}, and \frac{2}{5}$ the probabilities that he will be late are $\frac{1}{4}, \frac{1}{3} and \frac{1}{12}$ 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

$\frac{1}{2}$

$\frac{1}{3}$

$\frac{2}{3}$

$\frac{3}{5}$

answer is A.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

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

L-Late $P (\frac{L}{E_{1}}) = \frac{1}{4}, P (\frac{L}{E_{2}}) = \frac{1}{3}, P (\frac{L}{E_{3}}) = \frac{1}{12}, P (\frac{L}{E_{4}}) = 0$

WE have to find $P (\frac{E_{1}}{L})$

By Bayes theorem $P (\frac{E_{1}}{L})$ $= \frac{P (E_{1}) P (\frac{L}{E_{1}})}{P (E_{1}) P (\frac{L}{E_{1}}) + P (E_{2}) P (\frac{L}{E_{2}}) + P (E_{3}) P (\frac{L}{E_{3}}) + P (E_{4}) P (\frac{L}{E_{4}})}$

$= \frac{\frac{3}{10} . \frac{1}{4}}{\frac{3}{10} . \frac{1}{4} + \frac{1}{5} . \frac{1}{3} + \frac{1}{10} . \frac{1}{12} + \frac{2}{5} .0}$ $= \frac{\frac{3}{40}}{\frac{3}{40} + \frac{1}{15} + \frac{1}{120}} = \frac{\frac{3}{40}}{\frac{9 + 8 + 1}{120}} = \frac{3}{40} \times \frac{120}{18} = \frac{1}{2}$