Advertisements
Advertisements
Question
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 one white and one black
Advertisements
Solution
First Bag contains 5 white and 3 black balls
Total number of balls in the first bag 8 Second Bag contains 4 white and 6 black halls
Total number of balls in the second bag = 10
One ball is drawn from each bag.
P(getting one white and one black) = P( getting one white from the first bag or one white from the second bag) + P(getting one black from the first bag or one black from the second bag)
= `((""^5"C"_1)/(""^8"C"_1) xx (""^6"C"_1)/(""^10"C"_1)) + ((""^4"C"_1)/(""^10"C"_1) xx (""^3"C"_1)/(""^8"C"_1))`
= `(5/8 xx 6/10) + (4/10 xx 3/8)`
= `3/8 + 3/20`
= `(15 + 6)/40`
= `21/40`
APPEARS IN
RELATED QUESTIONS
A fair coin is tossed five times. Find the probability that it shows exactly three times head.
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.
A die is thrown three times. Events A and B are defined as below:
A : 5 on the first and 6 on the second throw.
B: 3 or 4 on the third throw.
Find the probability of B, given that A has already occurred.
40% students of a college reside in hostel and the remaining reside outside. At the end of the year, 50% of the hostelers got A grade while from outside students, only 30% got A grade in the examination. At the end of the year, a student of the college was chosen at random and was found to have gotten A grade. What is the probability that the selected student was a hosteler ?
Evaluate P(A ∪ B), if 2P(A) = P(B) = `5/13` and P(A | B) = `2/5`
Determine P(E|F).
A coin is tossed three times, where
E: at most two tails, F: at least one tail
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
Consider the experiment of throwing a die, if a multiple of 3 comes up, throw the die again and if any other number comes, toss a coin. Find the conditional probability of the event ‘the coin shows a tail’, given that ‘at least one die shows a 3’.
A and B are two events such that P (A) ≠ 0. Find P (B|A), if A ∩ B = Φ.
An urn contains 2 white and 2 black balls. A ball is drawn at random. If it is white, it is not replaced into the urn. Otherwise, it is replaced with another ball of the same colour. The process is repeated. Find the probability that the third ball is drawn is black.
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.
A bag contains 10 white balls and 15 black balls. Two balls are drawn in succession without replacement. What is the probability that, first is white and second is black?
If A and B are two independent events such that P(A ∪ B) = 0.6, P(A) = 0.2, find P(B)
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?
Choose the correct alternative:
If A and B are any two events, then the probability that exactly one of them occur is
If P(A) = 0.4, P(B) = 0.8 and P(B|A) = 0.6, then P(A ∪ B) is equal to ______.
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 ______.
If for two events A and B, P(A – B) = `1/5` and P(A) = `3/5`, then `P(B/A)` is equal to ______.
Compute P(A|B), if P(B) = 0.5 and P (A ∩ B) = 0.32.
If P(B) = `3/5`, P(A | B) = `1/2` and P(A ∪ B) = `4/5`, then P(A ∪ B) + P(A' ∪ B) =
