Advertisements
Advertisements
प्रश्न
A problem in statistics is given to three students A, B, and C. Their chances of solving the problem are `1/3`, `1/4`, and `1/5` respectively. If all of them try independently, what is the probability that, problem is not solved
उत्तर
Let A be the event that student A can solve the problem.
B be the event that student B can solve problem.
C be the event that student C can solve problem.
∴ P(A) = `1/3`, P(B) = `1/4` and P(C) = `1/5`
P(A') = 1 − P(A) = `1-1/3=2/3`
P(B') = 1 − P(B) = `1-1/4=3/4`
P(C') = 1 − P(C) = `1-1/5=4/5`
Since A, B, C are independent events
∴ A', B', C' are also independent events
Let Y be the event that problem is not solved
P(Y) = P(A' ∩ B' ∩ C')
= P(A') × P(B') × P(C')
= `2/3xx3/4xx4/5`
= `2/5`
APPEARS IN
संबंधित प्रश्न
The probabilities of solving a specific problem independently by A and B are `1/3` and `1/5` respectively. If both try to solve the problem independently, find the probability that the problem is solved.
The odds against a husband who is 55 years old living till he is 75 is 8: 5 and it is 4: 3 against his wife who is now 48, living till she is 68. Find the probability that the couple will be alive 20 years hence.
The odds against a husband who is 55 years old living till he is 75 is 8: 5 and it is 4: 3 against his wife who is now 48, living till she is 68. Find the probability that at least one of them will be alive 20 years hence.
The odds against student X solving a business statistics problem are 8: 6 and odds in favour of student Y solving the same problem are 14: 16 What is the probability that neither solves the problem?
A, B, and C try to hit a target simultaneously but independently. Their respective probabilities of hitting the target are `3/4, 1/2` and `5/8`. Find the probability that the target
- is hit exactly by one of them
- is not hit by any one of them
- is hit
- is exactly hit by two of them
The probability that a student X solves a problem in dynamics is `2/5` and the probability that student Y solves the same problem is `1/4`. What is the probability that
- the problem is not solved
- the problem is solved
- the problem is solved exactly by one of them
Two hundred patients who had either Eye surgery or Throat surgery were asked whether they were satisfied or unsatisfied regarding the result of their surgery.
The following table summarizes their response:
| Surgery | Satisfied | Unsatisfied | Total |
| Throat | 70 | 25 | 95 |
| Eye | 90 | 15 | 105 |
| Total | 160 | 40 | 200 |
If one person from the 200 patients is selected at random, determine the probability the person had Throat surgery given that the person was unsatisfied.
Solve the following:
If P(A) = `"P"("A"/"B") = 1/5, "P"("B"/"A") = 1/3` the find `"P"("A'"/"B")`
Solve the following:
Find the probability that a year selected will have 53 Wednesdays
Solve the following:
For three events A, B and C, we know that A and C are independent, B and C are independent, A and B are disjoint, P(A ∪ C) = `2/3`, P(B ∪ C) = `3/4`, P(A ∪ B ∪ C) = `11/12`. Find P(A), P(B) and P(C)
The probability of simultaneous occurrence of at least one of two events A and B is p. If the probability that exactly one of A, B occurs is q, then prove that P(A′) + P(B′) = 2 – 2p + q.
Two dice are thrown together and the total score is noted. The events E, F and G are ‘a total of 4’, ‘a total of 9 or more’, and ‘a total divisible by 5’, respectively. Calculate P(E), P(F) and P(G) and decide which pairs of events, if any, are independent.
If A and B are two events such that P(A) = `1/2`, P(B) = `1/3` and P(A/B) = `1/4`, P(A' ∩ B') equals ______.
If two events are independent, then ______.
If A and B are independent, then P(exactly one of A, B occurs) = P(A)P(B') + P(B)P(A')
If A and B are two events such that P(A) > 0 and P(A) + P(B) >1, then P(B|A) ≥ `1 - ("P"("B'"))/("P"("A"))`
Let A and B be two events. If P(A | B) = P(A), then A is ______ of B.
If A, B are two events such that `1/8 ≤ P(A ∩ B) ≤ 3/8` then
Let A and B be independent events P(A) = 0.3 and P(B) = 0.4. Find P(A ∩ B)
Given two independent events A and B such that P(A) = 0.3, P(B) = 0.6 and P(A' ∩ B') is ______.
