Advertisements
Advertisements
Question
In an examination, 30% of students have failed in subject I, 20% of the students have failed in subject II and 10% have failed in both subject I and subject II. A student is selected at random, what is the probability that the student has failed in at least one subject?
Solution
Let A be the event that the student failed in Subject I
B be the event that the student failed in Subject II
Then P(A) = 30% = `30/100`
P(B) = 20% = `20/100`
And P(A ∩ B) = 10% = `10/100 `
P (student failed in at least one subject)
= P(A ∪ B) = P(A) + P(B) – P(A∩ B)
= `30/100 + 20/100 - 10/100`
= `40/100`
= 0.40
APPEARS IN
RELATED QUESTIONS
In a game, a man wins Rs 5 for getting a number greater than 4 and loses Rs 1 otherwise, when a fair die is thrown. The man decided to thrown a die thrice but to quit as and when he gets a number greater than 4. Find the expected value of the amount he wins/loses
Determine P(E|F).
A coin is tossed three times, where
E: at least two heads, F: at most two heads
A black and a red dice are rolled.
Find the conditional probability of obtaining a sum greater than 9, given that the black die resulted in a 5.
A fair die is rolled. Consider events E = {1, 3, 5}, F = {2, 3} and G = {2, 3, 4, 5} Find P (E|G) and P (G|E)
An instructor has a question bank consisting of 300 easy True/False questions, 200 difficult True/False questions, 500 easy multiple choice questions and 400 difficult multiple choice questions. If a question is selected at random from the question bank, what is the probability that it will be an easy question given that it is a multiple-choice question?
A die is tossed thrice. Find the probability of getting an odd number at least once.
Five dice are thrown simultaneously. If the occurrence of an odd number in a single dice is considered a success, find the probability of maximum three successes.
Three cards are drawn at random (without replacement) from a well-shuffled pack of 52 playing cards. Find the probability distribution of the number of red cards. Hence, find the mean of the distribution.
A pair of dice is thrown. If sum of the numbers is an even number, what is the probability that it is a perfect square?
From a pack of well-shuffled cards, two cards are drawn at random. Find the probability that both the cards are diamonds when first card drawn is kept aside
One bag contains 5 white and 3 black balls. Another bag contains 4 white and 6 black balls. If one ball is drawn from each bag, find the probability that both are white
Suppose the chances of hitting a target by a person X is 3 times in 4 shots, by Y is 4 times in 5 shots, and by Z is 2 times in 3 shots. They fire simultaneously exactly one time. What is the probability that the target is damaged by exactly 2 hits?
A die is thrown nine times. If getting an odd number is considered as a success, then the probability of three successes is ______
Three machines E1, E2, E3 in a certain factory produced 50%, 25% and 25%, respectively, of the total daily output of electric tubes. It is known that 4% of the tubes produced one each of machines E1 and E2 are defective, and that 5% of those produced on E3 are defective. If one tube is picked up at random from a day’s production, calculate the probability that it is defective.
Find the probability that in 10 throws of a fair die a score which is a multiple of 3 will be obtained in at least 8 of the throws.
If A and B are two events such that P(A) = `1/3`, P(B) = `1/5` and P(A ∪ B) = `1/2`, then P(A|B') + P(B|A') is equal to ______.
Read the following passage:
|
Recent studies suggest the roughly 12% of the world population is left-handed.
Assuming that P(A) = P(B) = P(C) = P(D) = `1/4` and L denotes the event that child is left-handed. |
Based on the above information, answer the following questions:
- Find `P(L/C)` (1)
- Find `P(overlineL/A)` (1)
- (a) Find `P(A/L)` (2)
OR
(b) Find the probability that a randomly selected child is left-handed given that exactly one of the parents is left-handed. (2)
If A and B are two independent events such that P(A) = `1/3` and P(B) = `1/4`, then `P(B^'/A)` is ______.
A Problem in Mathematics is given to the three students A, B and C. Their chances of solving the problem are `1/2, 1/3` and `1/4` respectively. Find the probability that exactly two students will solve the problem.
Compute P(A|B), if P(B) = 0.5 and P (A ∩ B) = 0.32.
