The probability that a husband and his wife will be alive in 10 year's time are 0.7 and 0.8 respectively.what is the probability that at the same time none will be alive
Answers
Answer:As others have stated, this question cannot be concretely answered from the information given. However I'd like to go a little further than the other answers by using life expectancy tables with some assumptions, just for interest.
Using UK mortality rates, and assuming A and B are both males; then I can estimate that A is around 57 years old. That's because it's at age 57 that the chance of a male surviving for the next 20 years is closest to 0.7.
This is derived from the mortality figures that can be found here (Excel download): Page on ons.gov.uk
With a similar approach, I can estimate that B is approximately 64.
Assuming independence of probabilities, then the chance of A and B both living another 29 years, then becomes the P(A living to at least 86|he is 57)*P(B living to 93|he is 64).
Again deriving from the mortality tables, the probability of a 57 year old UK male surviving to 86 is 0.36. The probability of a 64 year old surviving to 93 is 0.11. Therefore the probability that both live for another 29 years is 0.36 x 0.11 = 0.039. That's spurious precision given the crudity of the interpolation I have done on the mortality rates, so call it 0.04.
If we assume A and B are both women instead, then we would estimate A to be 61 and B to be 66. The probabilities that A and B survive another 29 years become 0.30 & 0.124 respectively giving a combined probability of again 0.04.
Note: the bucketing within the mortality rates data introduces inaccuracy into the above estimates. This isn't too bad for the 5 year buckets up to 85, but bucketing all over 85 year olds into one mortality rate means significantly over-estimating the mortality rate for those in their late 80s, which will have impacted the above calculations (brought the probability down a little). Also of course, these are mortality rates as of 2013. We might expect rates to continue to improve, in which case our current 57 year old male would have a better probability of living to 86 than given. This answer was just an illustrative exploration, not a bone fide estimate.
Step-by-step explanation: