Advertisements
Advertisements
Question
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.
Advertisements
Solution
Let A be the event that husband would be alive after 20 years.
Odds against A are 8: 5
∴ The probability of occurrence of event A is given by
P(A) = `5/(8 + 5) = 5/13`
∴ P(A') = 1 – P(A) = `1 - 5/13 = 8/13`
Let B be the event that wife would be alive after 20 years.
Odds against B are 4: 3
∴ The probability of occurrence of event B is given by
P(B) = `3/(4 + 3) = 3/7`
∴ P(B') = 1 – P(B) = `1 - 3/7 = 4/7`
Since A and B are independent events
∴ A' and B' are also independent events
Let X be the event that both will be alive after 20 years.
∴ P(X) = (A ∩ B)
∴ P(X) = P(A).P(B) = `5/13 xx 3/7 = 15/91`
APPEARS IN
RELATED QUESTIONS
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.
If A and B are two events such that `P(A) = 1/4, P(B) = 1/2 and P(A ∩ B) = 1/8`, find P (not A and not B).
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)
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 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.
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?
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:
A machine produces parts that are either good (90%), slightly defective (2%), or obviously defective (8%). Produced parts get passed through an automatic inspection machine, which is able to detect any part that is obviously defective and discard it. What is the quality of the parts that make it throught the inspection machine and get shipped?
Let A and B be two independent events. Then P(A ∩ B) = P(A) + P(B)
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 A and B are two events and A ≠ Φ, B ≠ Φ, then ______.
If A and B are mutually exclusive events, then they will be independent also.
If A and B are two independent events then P(A and B) = P(A).P(B).
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 = ______.
One card is drawn at random from a well-shuffled deck of 52 cards. In which of the following case is the events E and F independent?
E : ‘the card drawn is black’
F : ‘the card drawn is a king’
Two events 'A' and 'B' are said to be independent if
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 ______.
Given two events A and B such that (A/B) = 0.25 and P(A ∩ B) = 0.12. The value P(A ∩ B') is ______.
