Advertisements
Advertisements
प्रश्न
10% of the bulbs produced in a factory are of red colour and 2% are red and defective. If one bulb is picked up at random, determine the probability of its being defective if it is red.
Advertisements
उत्तर
Let A and B be the events that the bulb is red and defective, respectively
P(A) = `10/100 = 1/10`.
P(A ∩ B) = `2/100 = 1/50`
P(B|A) = `("P"("A" ∩ "B"))/("P"("A"))`
= `1/50 xx 10/1`
= `1/5`
Thus the probability of the picked up bulb of its being defective, if it is red, is `1/5`.
APPEARS IN
संबंधित प्रश्न
A bag contains 4 balls. Two balls are drawn at random (without replacement) and are found to be white. What is the probability that all balls in the bag are white?
If `P(A) = 3/5 and P(B) = 1/5` , find P (A ∩ B) if A and B are independent events.
A fair coin and an unbiased die are tossed. Let A be the event ‘head appears on the coin’ and B be the event ‘3 on the die’. Check whether A and B are independent events or not.
In a race, the probabilities of A and B winning the race are `1/3` and `1/6` respectively. Find the probability of neither of them winning the race.
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.
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, exactly two students solve the problem?
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 chance that the problem will be solved, if they try independently?
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 follwoing 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 that the person was satisfied given that the person had Throat surgery.
Two dice are thrown together. Let A be the event 'getting 6 on the first die' and B be the event 'getting 2 on the second die'. Are the events A and B independent?
A bag contains 3 yellow and 5 brown balls. Another bag contains 4 yellow and 6 brown balls. If one ball is drawn from each bag, what is the probability that, the balls are of different color?
Solve the following:
If P(A ∩ B) = `1/2`, P(B ∩ C) = `1/3`, P(C ∩ A) = `1/6` then find P(A), P(B) and P(C), If A,B,C are independent events.
Solve the following:
Let A and B be independent events with P(A) = `1/4`, and P(A ∪ B) = 2P(B) – P(A). Find P(B)
Solve the following:
Let A and B be independent events with P(A) = `1/4`, and P(A ∪ B) = 2P(B) – P(A). 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)
If A and B are independent events such that 0 < P(A) < 1 and 0 < P(B) < 1, then which of the following is not correct?
Let A and B be two independent events. Then P(A ∩ B) = P(A) + P(B)
Refer to Question 1 above. If the die were fair, determine whether or not the events A and B are independent.
The probability that at least one of the two events A and B occurs is 0.6. If A and B occur simultaneously with probability 0.3, evaluate `"P"(bar"A") + "P"(bar"B")`
Let E1 and E2 be two independent events such that P(E1) = P1 and P(E2) = P2. Describe in words of the events whose probabilities are: P1P2
Let E1 and E2 be two independent events such that P(E1) = P1 and P(E2) = P2. Describe in words of the events whose probabilities are: (1 – P1) P2
Let E1 and E2 be two independent events such that P(E1) = P1 and P(E2) = P2. Describe in words of the events whose probabilities are: 1 – (1 – P1)(1 – P2)
Two dice are tossed. Find whether the following two events A and B are independent: A = {(x, y): x + y = 11} B = {(x, y): x ≠ 5} where (x, y) denotes a typical sample point.
If A and B are such events that P(A) > 0 and P(B) ≠ 1, then P(A′|B′) equals ______.
If A and B are two independent events with P(A) = `3/5` and P(B) = `4/9`, then P(A′ ∩ B′) equals ______.
If A and B are two independent events with P(A) = `3/5` and P(B) = `4/9`, then P(A′ ∩ B′) equals ______.
Two events E and F are independent. If P(E) = 0.3, P(E ∪ F) = 0.5, then P(E|F) – P(F|E) equals ______.
If A and B are mutually exclusive events, then they will be independent also.
If A and B are two events such that P(A|B) = p, P(A) = p, P(B) = `1/3` and P(A ∪ B) = `5/9`, then p = ______.
If A, B are two events such that `1/8 ≤ P(A ∩ B) ≤ 3/8` then
If P(A) = `3/5` and P(B) = `1/5`, find P(A ∩ B), If A and B are independent events.
Events A and Bare such that P(A) = `1/2`, P(B) = `7/12` and `P(barA ∪ barB) = 1/4`. Find whether the events A and B are independent or not.
