Advertisements
Advertisements
प्रश्न
An insurance company insured 3000 cyclists, 6000 scooter drivers, and 9000 car drivers. The probability of an accident involving a cyclist, a scooter driver, and a car driver are 0⋅3, 0⋅05 and 0⋅02 respectively. One of the insured persons meets with an accident. What is the probability that he is a cyclist?
उत्तर
Let E1, E2, and E3 be the respective events that the driver is a cyclist, a scooter driver, and a car driver.
Let A be the event that the person meets with an accident.
There are 3000 cyclists, 6000 scooter drivers, and 9000 car drivers.
Total number of drivers = 3000 + 6000 + 9000 = 18000
P(E1) = P(driver is a cyclist) `=3000/1800=1/6`
P(E2) = P(driver is a scooter driver) `=6000/18000=1/3`
P(E3) = P(driver is a car driver)`=9000/18000=1/2`
P (A|E1) = P (cyclist met with an accident) = 0.3
P (A|E2) = P (scooter driver met with an accident) = 0.05
P (A|E3) = P (car driver met with an accident) = 0.02
The probability that the driver is a cyclist, given that he met with an accident, is given by P (E1|A).
P (E1|A) `=("P"("E"_1)."P"("A"|"E"_1))/("P"("E"_1)."P"("A"|"E"_1)+"P"("E"_2)."P"("A"|"E"_2)+"P"("E"_3)."P"("A"|"E"_3)`
`=(1/6xx0.3)/(1/6xx0.3+1/3xx0.05+1/2xx0.02)`
`=(1/6xx30/100)/(1/6xx30/100+2/6xx5/100+3/6xx2/100)`
`=30/46=15/23`
APPEARS IN
संबंधित प्रश्न
A and B throw a die alternatively till one of them gets a number greater than four and wins the game. If A starts the game, what is the probability of B winning?
An experiment succeeds thrice as often as it fails. Find the probability that in the next five trials, there will be at least 3 successes.
A couple has two children. Find the probability that both the children are (i) males, if it is known that at least one of the children is male. (ii) females, if it is known that the elder child is a female.
A card is drawn from a well-shuffled deck of 52 cards and then a second card is drawn. Find the probability that the first card is a heart and the second card is a diamond if the first card is not replaced.
If P (A) = \[\frac{7}{13}\], P (B) = \[\frac{9}{13}\] and P (A ∩ B) = \[\frac{4}{13}\], find P (A/B).
A die is thrown twice and the sum of the numbers appearing is observed to be 8. What is the conditional probability that the number 5 has appeared at least once?
Given two independent events A and B such that P (A) = 0.3 and P (B) = 0.6. Find \[P \overline A \cup \overline B \] .
The probability that A hits a target is 1/3 and the probability that B hits it, is 2/5, What is the probability that the target will be hit, if each one of A and B shoots at the target?
An anti-aircraft gun can take a maximum of 4 shots at an enemy plane moving away from it. The probabilities of hitting the plane at the first, second, third and fourth shot are 0.4, 0.3, 0.2 and 0.1 respectively. What is the probability that the gun hits the plane?
Two dice are thrown together and the total score is noted. The event E, F and G are "a total of 4", "a total of 9 or more", and "a total divisible by 5", respectively. Calculate P(E), P(F) and P(G) and decide which pairs of events, if any, are independent.
A bag contains 3 red and 5 black balls and a second bag contains 6 red and 4 black balls. A ball is drawn from each bag. Find the probability that one is red and the other is black.
Two balls are drawn at random with replacement from a box containing 10 black and 8 red balls. Find the probability that both the balls are red.
A speaks truth in 75% and B in 80% of the cases. In what percentage of cases are they likely to contradict each other in narrating the same incident?
Kamal and Monica appeared for an interview for two vacancies. The probability of Kamal's selection is 1/3 and that of Monika's selection is 1/5. Find the probability that
(i) both of them will be selected
(ii) none of them will be selected
(iii) at least one of them will be selected
(iv) only one of them will be selected.
Two cards are drawn from a well shuffled pack of 52 cards, one after another without replacement. Find the probability that one of these is red card and the other a black card?
Tickets are numbered from 1 to 10. Two tickets are drawn one after the other at random. Find the probability that the number on one of the tickets is a multiple of 5 and on the other a multiple of 4.
A, B, and C are independent witness of an event which is known to have occurred. Aspeaks the truth three times out of four, B four times out of five and C five times out of six. What is the probability that the occurrence will be reported truthfully by majority of three witnesses?
Three persons A, B, C throw a die in succession till one gets a 'six' and wins the game. Find their respective probabilities of winning.
There are 3 red and 5 black balls in bag 'A'; and 2 red and 3 black balls in bag 'B'. One ball is drawn from bag 'A' and two from bag 'B'. Find the probability that out of the 3 balls drawn one is red and 2 are black.
Fatima and John appear in an interview for two vacancies for the same post. The probability of Fatima's selection is \[\frac{1}{7}\] and that of John's selection is \[\frac{1}{5}\] What is the probability that
(i) both of them will be selected?
(ii) only one of them will be selected?
(iii) none of them will be selected?
A four digit number is formed using the digits 1, 2, 3, 5 with no repetitions. Write the probability that the number is divisible by 5.
In a competition A, B and C are participating. The probability that A wins is twice that of B, the probability that B wins is twice that of C. Find the probability that A losses.
If A and B are two independent events, then write P (A ∩ \[B\] ) in terms of P (A) and P (B).
If A and B are independent events such that P(A) = p, P(B) = 2p and P(Exactly one of Aand B occurs) = \[\frac{5}{9}\], then find the value of p.
If one ball is drawn at random from each of three boxes containing 3 white and 1 black, 2 white and 2 black, 1 white and 3 black balls, then the probability that 2 white and 1 black balls will be drawn is
Five persons entered the lift cabin on the ground floor of an 8 floor house. Suppose that each of them independently and with equal probability can leave the cabin at any floor beginning with the first, then the probability of all 5 persons leaving at different floors is
Mark the correct alternative in the following question:
\[\text{ If A and B are two events such that } P\left( A \right) = \frac{1}{2}, P\left( B \right) = \frac{1}{3}, P\left( A|B \right) = \frac{1}{4}, \text{ then } P\left( A \cap B \right) \text{ equals} \]
Mark the correct alternative in the following question:
\[\text{ If the events A and B are independent, then } P\left( A \cap B \right) \text{ is equal to } \]
Mark the correct alternative in the following question:A flash light has 8 batteries out of which 3 are dead. If two batteries are selected without replacement and tested, then the probability that both are dead is
Mark the correct alternative in the following question:
A die is thrown and a card is selected at random from a deck of 52 playing cards. The probability of getting an even number of the die and a spade card is
