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A bag contains 5 white, 7 red and 8 black balls. If four balls are drawn one by one without replacement, find the probability of getting all white balls.
A die is rolled twice and the sum of the numbers appearing on them is observed to be 7. What is the conditional probability that the number 2 has appeared at least once?
A bag contains 19 tickets, numbered from 1 to 19. A ticket is drawn and then another ticket is drawn without replacement. Find the probability that both tickets will show even numbers.
Two integers are selected at random from integers 1 to 11. If the sum is even, find the probability that both the numbers are odd.
A die is thrown twice and the sum of the numbers appearing is observed to be 6. What is the probability that the number 4 has appeared at least once?
A can solve 90% of the problems given in a book and B can solve 70%. What is the probability that at least one of them will solve the problem, selected at random from the book?
Two dice are thrown. Find the probability of getting an odd number on the first die and a multiple of 3 on the other.
In Insurance Company insured 2000 scooter drives, 4000 car drivers and 6000 truck drivers. The probability of an accident involving a scooter driver, car driver and a truck is 0.01, 0.03 and 0.15 respectively. One of the insured person meets with an accident. What is the probability that he is a scooter driver?
A black and a red die are rolled.
(i) Find the conditional probability of obtaining a sum greater than 9, given that the black die resulted in a 5.
(ii) Find the conditional probability of obtaining the sum 8, given that the red die resulted in a number less than 4.
A couple has two children. Find the probability that
(i) Both the children are boys, if it is known that the older child is a boy.
(ii) Both the children are girls, if it is known that the older child is girl.
(iii) Both the children are boys, if it is known that at least one of the children is a boy.
Find the probability of drawing a diamond card in each of the two consecutive draws from a well shuffled pack of cards, if the card drawn is not replaced after the first drawn.
A police-man fires four bullets on a dacoit. The probability that the dacoit will be killed by one bullet is 0.6. What is the probability that the dacoit is still alive?
Two integers are selected at random from integers 1 through 11. If the sum is even, find the probability that both the numbers are odd.
In a test, an examinee either guesses or copies or knows the answer to a multiple choice question with four choices. The probability that he makes a guess is 1/3 and the probability that he copies the answer is 1/6. The probability that his answer is correct, given that he copied it, is 1/8. Find the probability that he knew the answer to the question, given that he correctly answered it.
Three distinguishable balls are distributed in three cells. Find the conditional probability that all the three occupy the same cell, given that at least two of them are in the same cell.
A problem in mathematics is given to 3 students whose chance of solving it are 1/2, 1/3, 1/4. What is the probability that the problem is solved?
A company has estimated that the probabilities of success for three products introduced in the market are 1/3, 2/5 and 2/3 respectively. Assuming independence, find
(i) the probability that the three products are successful.
(ii) the probability that none of the products is successful.
Probabilities of solving a specific problem independently by A and B are 1/2 and 1/3 respectively. If both try to solve the problem independently, find the probability that
(i) The problem is solved
(ii) exactly one of them solves the problem.
In a school, there are 1000 students, out of which 430 are girls. It is known that out of 430, 10% of the girls study in class XII. What is the probability that a student chosen randomly studies in class XII given that the chosen student is a girl?
A man is known to speak truth 3 out of 4 times. He throws a die and reports that it is a six. Find the probability that it is actually a six.