Advertisements
Advertisements
प्रश्न
Two balls are drawn at random with replacement from a box containing 10 black and 8 red balls. Find the probability that
- both balls are red.
- first ball is black and second is red.
- one of them is black and other is red.
Advertisements
उत्तर
Let R = the event of drawing a red ball; B = the event of drawing a black ball
i. Probability of getting a red ball in the first draw P(R) = `8/(10 + 8) = 8/18 = 4/9`
Because the ball is put back again.
∴ The probability of getting a red ball in the second draw P(R) = `4/9`
∴ The probability of both balls being red = P(R). P(R) = `4/9 xx 4/9 = 16/81`
ii. Probability of getting a black ball in the first draw P(B) = `10/18 = 5/9`
The probability of getting a red ball in the second draw P(R) = `4/9`
∴ P(first black and second red) = P(B) . P(R) = `5/9 xx 4/9 = 20/81`
iii. P(one black and one red) = P(first black and second red) + P(first red and second black)
= `5/9 . 4/9 + 4/9 . 5/9`
= `40/81`
APPEARS IN
संबंधित प्रश्न
Suppose that 80% of all families own a television set. If 5 families are interviewed at random, find the probability that
a. three families own a television set.
b. at least two families own a television set.
Determine P(E|F).
Mother, father and son line up at random for a family picture
E: son on one end, F: father in middle
A fair die is rolled. Consider events E = {1, 3, 5}, F = {2, 3} and G = {2, 3, 4, 5} Find P (E|F) and P (F|E)
If P(A) = `1/2`, P(B) = 0, then P(A|B) is ______.
A die is tossed thrice. Find the probability of getting an odd number at least once.
A and B are two events such that P (A) ≠ 0. Find P (B|A), if A is a subset of B.
In a game, a man wins a rupee for a six and loses a rupee for any other number when a fair die is thrown. The man decided to throw a die thrice but to quit as and when he gets a six. Find the expected value of the amount he wins/loses.
A box has 20 pens of which 2 are defective. Calculate the probability that out of 5 pens drawn one by one with replacement, at most 2 are defective.
Two balls are drawn from an urn containing 3 white, 5 red and 2 black balls, one by one without replacement. What is the probability that at least one ball is red?
If events A and B are independent, such that `P(A)= 3/5`, `P(B)=2/3` 'find P(A ∪ B).
Two dice are thrown simultaneously, If at least one of the dice show a number 5, what is the probability that sum of the numbers on two dice is 9?
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?
A bag contains 10 white balls and 15 black balls. Two balls are drawn in succession without replacement. What is the probability that, one is white and other is black?
An urn contains 4 black, 5 white, and 6 red balls. Two balls are drawn one after the other without replacement, What is the probability that at least one ball is black?
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
Can two events be mutually exclusive and independent simultaneously?
If A and B are two events such that P(A ∪ B) = 0.7, P(A ∩ B) = 0.2, and P(B) = 0.5, then show that A and B are independent
A problem in Mathematics is given to three students whose chances of solving it are `1/3, 1/4` and `1/5`. What is the probability that the problem is solved?
A problem in Mathematics is given to three students whose chances of solving it are `1/3, 1/4` and `1/5`. What is the probability that exactly one of them will solve it?
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
A year is selected at random. What is the probability that it is a leap year which contains 53 Sundays
Choose the correct alternative:
A letter is taken at random from the letters of the word ‘ASSISTANT’ and another letter is taken at random from the letters of the word ‘STATISTICS’. The probability that the selected letters are the same is
Choose the correct alternative:
If two events A and B are independent such that P(A) = 0.35 and P(A ∪ B) = 0.6, then P(B) is
In a multiple-choice question, there are three options out of which only one is correct. A person is guessing the answer at random. If there are 7 such questions, then the probability that he will get exactly 4 correct answers is ______
If X denotes the number of ones in five consecutive throws of a dice, then P(X = 4) is ______
Let A and B be two events. If P(A) = 0.2, P(B) = 0.4, P(A ∪ B) = 0.6, then P(A|B) is equal to ______.
A bag contains 6 red and 5 blue balls and another bag contains 5 red and 8 blue balls. A ball is drawn from the first bag and without noticing its colour is placed in the second bag. If a ball is drawn from the second bag, then find the probability that the drawn ball is red in colour.
A bag contains 3 red and 4 white balls and another bag contains 2 red and 3 white balls. If one ball is drawn from the first bag and 2 balls are drawn from the second bag, then find the probability that all three balls are of the same colour.
A pack of cards has one card missing. Two cards are drawn randomly and are found to be spades. The probability that the missing card is not a spade, is ______.
Let A and B be two non-null events such that A ⊂ B. Then, which of the following statements is always correct?
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 ______.
If A and B are events and \[P(B) \neq 0\], which expression gives \[P(A \mid B)\]?
If A and B are events and \[P(A) \neq 0\], which expression gives \[P(B \mid A)\]?
Which statement is the multiplication rule for two events A and B?
For \[E=\{(b,b)\}\] and \[F=\{(b,b),(g,b),(b,g)\}\], what are \[E\cap F\], \[P(E\cap F)\], and \[P(F)\]?
