Advertisements
Advertisements
प्रश्न
Suppose the chances of hitting a target by a person X is 3 times in 4 shots, by Y is 4 times in 5 shots, and by Z is 2 times in 3 shots. They fire simultaneously exactly one time. What is the probability that the target is damaged by exactly 2 hits?
Advertisements
उत्तर
Given
Probability X hitting the target P(X) = `3/4`
Probability Y hitting the target P(Y) = `4/5`
Probability Z hitting the target P(Z) = `2/3`
`"P"(bar"X")` = 1 – P(X) = `1 - 3/4 = 1/4`
`"P"(bar"Y")` = 1 – P(Y) = `1 - 4/5 = 1/5`
`"P"(bar"Z")` = 1 – P(Z) = `1 - 2/3 = 1/3`
Probability hitting the target exactly by 2 hits
= `"P"[("X" ∩ "Y" ∩ bar"Z") ∪ (bar"X" ∩ "Y" ∩ "Z") ∪ ("X" ∩bar"Y" ∩ "Z")]`
= `"P"("X" ∩ "Y" ∩ bar"Z") + "P"(bar"X" ∩ "Y" ∩ "Z") + "P"("X" ∩bar"Y" ∩ "Z")`
= `"P"("X") "P"("Y") "P"(bar"Z") + "P"(bar"X") "P"("Y") "P"("Z") + "P"("X") "P"(bar"Y") "P"("Z")`
= `3/4 xx 4/5 xx 1/3 + 1/4 xx 4/5 xx 2/3 + 3/4 xx 1/5 xx 2/3`
= `(12 + 8 + 6)/60`
= `26/60`
= `13/30`
APPEARS IN
संबंधित प्रश्न
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.
A bag X contains 4 white balls and 2 black balls, while another bag Y contains 3 white balls and 3 black balls. Two balls are drawn (without replacement) at random from one of the bags and were found to be one white and one black. Find the probability that the balls were drawn from bag Y.
Determine P(E|F).
A coin is tossed three times, where
E: head on third toss, F: heads on first two tosses
A and B are two events such that P (A) ≠ 0. Find P (B|A), if A ∩ B = Φ.
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.
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?
In an examination, 30% of students have failed in subject I, 20% of the students have failed in subject II and 10% have failed in both subject I and subject II. A student is selected at random, what is the probability that the student has failed in subject I, if it is known that he is failed in subject II?
In an examination, 30% of students have failed in subject I, 20% of the students have failed in subject II and 10% have failed in both subject I and subject II. A student is selected at random, what is the probability that the student has failed in at least one subject?
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?
Select the correct option from the given alternatives :
Bag I contains 3 red and 4 black balls while another Bag II contains 5 red and 6 black balls. One ball is drawn at random from one of the bags and it is found to be red. The probability that it was drawn from Bag II
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
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 A and B are any two events, then the probability that exactly one of them occur is
Two dice are thrown. Find the probability that the sum of numbers appearing is more than 11, is ______.
The total number of ways in which 5 balls of different colours can be distributed among 3 persons so that each person gets at least one ball is ______
Three machines E1, E2, E3 in a certain factory produced 50%, 25% and 25%, respectively, of the total daily output of electric tubes. It is known that 4% of the tubes produced one each of machines E1 and E2 are defective, and that 5% of those produced on E3 are defective. If one tube is picked up at random from a day’s production, calculate the probability that it is defective.
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 ______.
If P(A ∩ B) = `7/10` and P(B) = `17/20`, then P(A|B) equals ______.
If P(A) = `3/10`, P(B) = `2/5` and P(A ∪ B) = `3/5`, then P(B|A) + P(A|B) equals ______.
If the sum of numbers obtained on throwing a pair of dice is 9, then the probability that number obtained on one of the dice is 4, is ______.
