Advertisements
Advertisements
Question
The odds against student X solving a business statistics problem are 8: 6 and odds in favour of student Y solving the same problem are 14: 16 What is the chance that the problem will be solved, if they try independently?
Advertisements
Solution
Let A be the event that X solves the problem B be the event that Y solves the problem.
Since the odds against student X solving the problem are 8: 6
∴ Probability of occurrence of event A is given by.
P(A) = `6/(8 + 6) = 6/14` and
P(A') = 1 – P(A) = `1 - 6/14 = 8/14`
Also, the odds in favour of student Y solving the problem are 14: 16
∴ Probability of occurrence of event B is given by
P(B) = `14/(14 + 16) = 14/30` and
P(B') = 1 – P(B) = `1 - 14/30 = 16/30`
Now A and B are independent events.
∴ A' and B' are independent events.
A' ∩ B' = Event that neither solves the problem
= P(A' ∩ B') = P(A') · P(B')
= `8/14 xx 16/30`
= `32/105`
A ∪ B = the event that the problem is solved
∴ P (problem will be solved) = P(A ∪ B)
= 1 – P(A ∪ B)`
= 1 – P(A' ∩ B')
= `1 - 32/105`
= `73/105`
APPEARS IN
RELATED QUESTIONS
In a race, the probabilities of A and B winning the race are `1/3` and `1/6` respectively. Find the probability of neither of them winning the race.
A fair die is rolled. If face 1 turns up, a ball is drawn from Bag A. If face 2 or 3 turns up, a ball is drawn from Bag B. If face 4 or 5 or 6 turns up, a ball is drawn from Bag C. Bag A contains 3 red and 2 white balls, Bag B contains 3 red and 4 white balls and Bag C contains 4 red and 5 white balls. The die is rolled, a Bag is picked up and a ball is drawn. If the drawn ball is red; what is the probability that it is drawn from Bag B?
A problem in statistics is given to three students A, B, and C. Their chances of solving the problem are `1/3`, `1/4`, and `1/5` respectively. If all of them try independently, what is the probability that, problem is not solved
An urn contains four tickets marked with numbers 112, 121, 122, 222 and one ticket is drawn at random. Let Ai (i = 1, 2, 3) be the event that ith digit of the number of the ticket drawn is 1. Discuss the independence of the events A1, A2, and A3.
The odds against student X solving a business statistics problem are 8: 6 and odds in favour of student Y solving the same problem are 14: 16 What is the probability that neither solves the problem?
Two dice are thrown together. Let A be the event 'getting 6 on the first die' and B be the event 'getting 2 on the second die'. Are the events A and B independent?
A family has two children. Find the probability that both the children are girls, given that atleast one of them is a girl.
The probability of simultaneous occurrence of at least one of two events A and B is p. If the probability that exactly one of A, B occurs is q, then prove that P(A′) + P(B′) = 2 – 2p + q.
Two dice are thrown together. Let A be the event ‘getting 6 on the first die’ and B be the event ‘getting 2 on the second die’. Are the events A and B independent?
Two dice are thrown together and the total score is noted. The events 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 and B are two events such that P(A) = `1/2`, P(B) = `1/3` and P(A ∩ B) = `1/4`. Find: `"P"("A'"/"B'")`
Three events A, B and C have probabilities `2/5, 1/3` and `1/2`, , respectively. Given that P(A ∩ C) = `1/5` and P(B ∩ C) = `1/4`, find the values of P(C|B) and P(A' ∩ C').
Two dice are tossed. Find whether the following two events A and B are independent: A = {(x, y): x + y = 11} B = {(x, y): x ≠ 5} where (x, y) denotes a typical sample point.
If two events are independent, then ______.
If A and B are independent events, then A′ and B′ are also independent
Events A and Bare such that P(A) = `1/2`, P(B) = `7/12` and `P(barA ∪ barB) = 1/4`. Find whether the events A and B are independent or not.
Let EC denote the complement of an event E. Let E1, E2 and E3 be any pairwise independent events with P(E1) > 0 and P(E1 ∩ E2 ∩ E3) = 0. Then `"P"(("E"_2^"C" ∩ "E"_3^"C")/"E"_1)` is equal to ______.
Five fair coins are tossed simultaneously. The probability of the events that at least one head comes up is ______.
The probability of the event A occurring is `1/3` and of the event B occurring is `1/2`. If A and B are independent events, then find the probability of neither A nor B occurring.
