Advertisements
Advertisements
प्रश्न
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?
Advertisements
उत्तर
Total number of balls = 10 + 15 = 25
Let S be event that two balls are drawn at random without replacement in succession
∴ n(S) = `""^25"C"_1xx""^24"C"_1` = 25 × 24
Let B be the event that one ball is white and other is black.
In this case, either 1st ball drawn is white and 2nd is black or 1st is black and 2nd is white.
First white ball can be drawn from 10 white balls in 10C1 ways and second black ball can be drawn from 15 black balls in 15C1 ways.
Similarly, first black ball from 15 black balls can be drawn in 15C1 ways and second white ball from 10 white balls can be drawn in 10C1 ways.
∴ n(B) = `""^10"C"_1""^15"C"_1+""^15"C"_1 ""^10"C"_1`
∴ P(B) = `("n"("B"))/("n"("S"))=(10xx15)/(25xx24)+(15xx10)/(25xx24)`
= `150/(25xx24)+150/(25xx24)`
= `300/(25xx24)`
= `1/2`
APPEARS IN
संबंधित प्रश्न
An insurance agent insures lives of 5 men, all of the same age and in good health. The probability that a man of this age will survive the next 30 years is known to be 2/3 . Find the probability that in the next 30 years at most 3 men will survive.
If P(A) = 0.8, P(B) = 0.5 and P(B|A) = 0.4, find P(A|B)
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.
If P(A) = `1/2`, P(B) = 0, then P(A|B) is ______.
A card is drawn from a well-shuffled pack of playing cards. What is the probability that it is either a spade or an ace or both?
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.
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.
In a college, 70% of students pass in Physics, 75% pass in Mathematics and 10% of students fail in both. One student is chosen at random. What is the probability that:
(i) He passes in Physics and Mathematics?
(ii) He passes in Mathematics given that he passes in Physics.
(iii) He passes in Physics given that he passes in Mathematics.
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?
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 exactly one of them will solve it?
The probability that a car being filled with petrol will also need an oil change is 0.30; the probability that it needs a new oil filter is 0.40; and the probability that both the oil and filter need changing is 0.15. If the oil had to be changed, what is the probability that a new oil filter is needed?
Given P(A) = 0.4 and P(A ∪ B) = 0.7 Find P(B) if A and B are mutually exclusive
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
If P(A) = `4/5`, and P(A ∩ B) = `7/10`, then P(B|A) is equal to ______.
If P(A) = `1/2`, P(B) = 0, then `P(A/B)` is
Let A and B be two non-null events such that A ⊂ B. Then, which of the following statements is always correct?
Compute P(A|B), if P(B) = 0.5 and P (A ∩ B) = 0.32.
