Advertisements
Advertisements
प्रश्न
Given two independent events A and B such that P (A) = 0.3, P (B) = 0.6. Find
- P (A and B)
- P(A and not B)
- P(A or B)
- P(neither A nor B)
Advertisements
उत्तर
It is given that P (A) = 0.3 and P (B) = 0.6
Also, A and B are independent events.
(i) ∴ P(A and B) = P(A) · P(B)
⇒ P(A ∩ B) = 0.3 × 0.6
P(A ∩ B) = 0.18
(ii) P(A and not B) = P(A ∩ B')
= P(A) - P(A ∩ B)
= 0.3 - 0.18
= 0.12
(iii) P(A or B) = P(A ∪ B)
= P(A) + P(B) - P(A ∩ B)
= 0.3 + 0.6 - 0.18
= 0.72
(iv) P(niether A nor B) = P(A' ∩ B')
= P((A' ∩ B'))
= 1 - P(A ∪ B)
= 1 - 0.72
= 0.28
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?
A die, whose faces are marked 1, 2, 3 in red and 4, 5, 6 in green is tossed. Let A be the event "number obtained is even" and B be the event "number obtained is red". Find if A and B are independent events.
Let E and F be events with `P(E) = 3/5, P(F) = 3/10 and P(E ∩ F) = 1/5`. Are E and F independent?
Events A and B are such that `P(A) = 1/2, P(B) = 7/12 and P("not A or not B") = 1/4` . State whether A and B are independent?
Two events, A and B, will be independent if ______.
If each element of a second order determinant is either zero or one, what is the probability that the value of the determinant is positive? (Assume that the individual entries of the determinant are chosen independently, each value being assumed with probability `1/2`).
A speaks the truth in 60% of the cases, while B is 40% of the cases. In what percent of cases are they likely to contradict each other in stating the same fact?
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 probability that a 50-year old man will be alive till age 60 is 0.83 and the probability that a 45-year old woman will be alive till age 55 is 0.97. What is the probability that a man whose age is 50 and his wife whose age is 45 will both be alive after 10 years?
One-shot is fired from each of the three guns. Let A, B, and C denote the events that the target is hit by the first, second and third guns respectively. assuming that A, B, and C are independent events and that P(A) = 0.5, P(B) = 0.6, and P(C) = 0.8, then find the probability that at least one hit is registered.
The odds against a certain event are 5: 2 and odds in favour of another independent event are 6: 5. Find the chance that at least one of the events will happen.
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
Select the correct option from the given alternatives :
The odds against an event are 5:3 and the odds in favour of another independent event are 7:5. The probability that at least one of the two events will occur is
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:
If P(A) = `"P"("A"/"B") = 1/5, "P"("B"/"A") = 1/3` the find `"P"("A'"/"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:
Let A and B be independent events with P(A) = `1/4`, and P(A ∪ B) = 2P(B) – P(A). Find `"P"("B'"/"A")`
Solve the following:
Consider independent trails consisting of rolling a pair of fair dice, over and over What is the probability that a sum of 5 appears before sum of 7?
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")`
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.
A and B are two events such that P(A) = `1/2`, P(B) = `1/3` and P(A ∩ B) = `1/4`. Find: `"P"("A'"/"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: P1 + P2 – 2P1P2
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 two events such that P(A) = `1/2`, P(B) = `1/3` and P(A/B) = `1/4`, P(A' ∩ B') equals ______.
If the events A and B are independent, then P(A ∩ B) is equal to ______.
Two cards are drawn at random and without replacement from a pack of 52 playing cards. Find the probability that both the cards are black.
Let A and B be independent events P(A) = 0.3 and P(B) = 0.4. Find P(A ∩ B)
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.
Let EC denote the complement of an event E. Let E1, E2 and E3 be any pairwise independent events with P(E1) > 0 and P(E1 ∩ E2 ∩ E3) = 0. Then `"P"(("E"_2^"C" ∩ "E"_3^"C")/"E"_1)` is equal to ______.
Given two independent events, if the probability that exactly one of them occurs is `26/49` and the probability that none of them occurs is `15/49`, then the probability of more probable of the two events is ______.
Two events E and F are independent when which conditional probability condition holds, provided \[P(F) \ne 0\]?
Which is the equivalent and most commonly used test for independent events E and F?
A die is thrown once. If F is the event that the number appearing is even, which set represents F?
For \[E\cap F=\{6\}\] when a die is thrown once, what is \[P(E\cap F)\]?
