Advertisements
Advertisements
प्रश्न
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.
उत्तर
Given:
Bag A: 1 white, 2 blue and 3 red balls
Bag B: 3 white, 3 blue and 2 red balls
Bag C: 2 white, 3 blue and 4 red balls
Let B1, B2, B3 and E be the events defined as
B1: Bag A is selected
B2: Bag B is selected
B3: Bag C is selected
And E: 1 white and 1 red ball is drawn
P(B1) = P(B2) = P(B3) = `1/3`
P(E/B1) = `(""^1C_1 xx^3C_1)/(""^6C_2) = 1/5`
P(E/B2) = `(""^3C_1 xx ^2C_1)/(""^8C_2) = 3/14`
P(E/B3) = `(""^2C_1 xx ^4C_1)/(""^9C_2) = 2/9`
Required probability = P(B1) × P(E/B1) + P(B2) × P(E/B2) + P(B3) × P(E/B3)
`= 1/3 xx 1/5 + 1/3 xx 3/14 + 1/3 xx 2/9`
`= 1/3 [1/5 + 3/14 + 2/9]`
`= 1/3 [(126 + 135 + 140)/(5xx14xx9)]`
`= 401/(3xx5xx14xx9) = 401/1890`
APPEARS IN
संबंधित प्रश्न
A coin is tossed 5 times. What is the probability of getting at least 3 heads?
A fair coin is tossed 8 times, find the probability of at least six heads
A coin is tossed 5 times. What is the probability that head appears an even number of times?
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.
A committee of 4 students is selected at random from a group consisting of 7 boys and 4 girls. Find the probability that there are exactly 2 boys in the committee, given that at least one girl must be there in the committee.
A coin and a die are tossed. State sample space of following event.
B: Getting a prime number.
Find total number of distinct possible outcomes n(S) of the following random experiment.
From a box containing 25 lottery tickets any 3 tickets are drawn at random.
Find total number of distinct possible outcomes n(S) of the following random experiment.
From a group of 4 boys and 3 girls, any two students are selected at random.
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.
Two dice are thrown. Write favourable outcomes for the following event.
R: Sum of the numbers on two dice is a prime number.
Also, check whether Events P and Q are mutually exclusive and exhaustive.
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.
Prove that P(A ∪ B) = `"P"("A" ∩ "B") + "P"("A" ∩ bar"B") + "P"(bar"A" ∩ bar"B")`
A bag contains 4 white and 5 black balls. Another bag contains 9 white and 7 black balls. A ball is transferred from the first bag to the second and then a ball is drawn at random from the second bag. Find the probability that the ball drawn is white.
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?
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?
Three bags contain a number of red and white balls as follows:
Bag 1:3 red balls, Bag 2:2 red balls and 1 white ball
Bag 3:3 white balls.
The probability that bag i will be chosen and a ball is selected from it is `"i"/6`, i = 1, 2, 3. What is the probability that a red ball will be selected?
Refer to Question 74 above. The probability that exactly two of the three balls were red, the first ball being red, is ______.
Assume that in a family, each child is equally likely to be a boy or a girl. A family with three children is chosen at random. The probability that the eldest child is a girl given that the family has at least one girl 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?
Two cards are drawn together from a pack of 52 cards. The probability that one is a spade and one is a heart, is?
Bag P contains 6 red and 4 blue balls and bag Q contains 5 red and 6 blue balls. A ball is transferred from bag P to bag Q and then a ball is drawn from bag Q. What is the probability that the ball drawn is blue?
Assertion (A): Two coins are tossed simultaneously. The probability of getting two heads, if it is known that at least one head comes up, is `1/3`.
Reason (R): Let E and F be two events with a random experiment, then `P(E/F) = (P(E ∩ F))/(P(E))`.
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?
