Advertisements
Advertisements
प्रश्न
There are two bags, one of which contains 3 black and 4 white balls while the other contains 4 black and 3 white balls. A die is thrown. If it shows up 1 or 3, a ball is taken from the Ist bag; but it shows up any other number, a ball is chosen from the second bag. Find the probability of choosing a black ball.
उत्तर
Let E1 be the event of selecting Bag I
And E2 be the event of selecting Bag II
Let E3 be the event that black ball is selected
∴ P(E1) = `2/6 = 1/3` and P(E2) = `1 - 1/3 = 2/3`
`"P"("E"_3/"E"_1) = 3/7` and `"P"("E"_3/"E"_2) = 4/7`
∴ P(E3) = `"P"("E"_1) * "P"("E"_3/"E"_1) + "P"("E"_2) * "P"("E"_3/"E"_2)`
= `1/3*3/7 + 2/3*4/7`
= `(3 + 8)/21`
= `11/21`
Hence, the required probability is `11/21`.
APPEARS IN
संबंधित प्रश्न
A pair of dice is thrown 6 times. If getting a total of 9 is considered a success, what is the probability of at least 5 successes?
A coin is tossed 5 times. What is the probability that head appears an even number of times?
Bag A contains 1 white, 2 blue and 3 red balls. Bag B contains 3 white, 3 blue and 2 red balls. Bag C contains 2 white, 3 blue and 4 red balls. One bag is selected at random and then two balls are drawn from the selected bag. Find the probability that the balls draw n are white and red.
One dialing certain telephone numbers assume that on an average, one telephone number out of five is busy, Ten telephone numbers are randomly selected and dialed. Find the probability that at least three of them will be busy.
A committee of 4 persons has to be chosen from 8 boys and 6 girls, consisting of at least one girl. Find the probability that the committee consists of more girls than boys.
Find total number of distinct possible outcomes n(S) of the following random experiment.
5 balls are randomly placed into 5 cells, such that each cell will be occupied.
Find total number of distinct possible outcomes n(S) of the following random experiment.
6 students are arranged in a row for a photograph.
Consider an experiment of drawing two cards at random from a bag containing 4 cards marked 5, 6, 7, and 8. Find the sample Space if cards are drawn with replacement.
Consider an experiment of drawing two cards at random from a bag containing 4 cards marked 5, 6, 7, and 8. Find the sample Space if cards are drawn without replacement.
There are 2 red and 3 black balls in a bag. 3 balls are taken out at random from the bag. Find the probability of getting 2 red and 1 black ball or 1 red and 2 black balls.
A car manufacturing factory has two plants, X and Y. Plant X manufactures 70% of cars and plant Y manufactures 30%. 80% of the cars at plant X and 90% of the cars at plant Y are rated of standard quality. A car is chosen at random and is found to be of standard quality. What is the probability that it has come from plant X?
A bag contains 5 red marbles and 3 black marbles. Three marbles are drawn one by one without replacement. What is the probability that at least one of the three marbles drawn be black, if the first marble is red?
Prove that P(A) = `"P"("A" ∩ "B") + "P"("A" ∩ bar"B")`
A box has 5 blue and 4 red balls. One ball is drawn at random and not replaced. Its colour is also not noted. Then another ball is drawn at random. What is the probability of second ball being blue?
Four cards are successively drawn without replacement from a deck of 52 playing cards. What is the probability that all the four cards are kings?
A die is thrown 5 times. Find the probability that an odd number will come up exactly three times.
The probability of a man hitting a target is 0.25. He shoots 7 times. What is the probability of his hitting at least twice?
A die is thrown three times. Let X be ‘the number of twos seen’. Find the expectation of X.
A and B throw a pair of dice alternately. A wins the game if he gets a total of 6 and B wins if she gets a total of 7. It A starts the game, find the probability of winning the game by A in third throw of the pair of dice.
An urn contains m white and n black balls. A ball is drawn at random and is put back into the urn along with k additional balls of the same colour as that of the ball drawn. A ball is again drawn at random. Show that the probability of drawing a white ball now does not depend on k.
By examining the chest X ray, the probability that TB is detected when a person is actually suffering is 0.99. The probability of an healthy person diagnosed to have TB is 0.001. In a certain city, 1 in 1000 people suffers from TB. A person is selected at random and is diagnosed to have TB. What is the probability that he actually has TB?
A flashlight has 8 batteries out of which 3 are dead. If two batteries are selected without replacement and tested, the probability that both are dead is ______.
Eight coins are tossed together. The probability of getting exactly 3 heads is ______.
A and B are two students. Their chances of solving a problem correctly are `1/3` and `1/4`, respectively. If the probability of their making a common error is, `1/20` and they obtain the same answer, then the probability of their answer to be correct is ______.
A box has 100 pens of which 10 are defective. What is the probability that out of a sample of 5 pens drawn one by one with replacement at most one is defective?
The letters of the word "ATTRACTION' are written randomly. The probability that no two T's appear together is
There are three machines and 2 of them are faulty. They are tested one by one in a random order till both the faulty machines are identified. What is the probability that only two tests are needed to identify the faulty machines?
