Question

The probabilties that a husband and wife will be alive 20 years from now are 0.7 and 0.8 . Find that in 20 years , husband will be a widower.​

Answer 1

$\huge{\textbf{QUESTION:}}$

The probabilties that a husband and wife will be alive 20 years from now are 0.7 and 0.8 . Find that in 20 years , husband will be a widower.

$\huge{\textbf{ANSWER:}}$

Let A be the event that a husband will be alive after 20 yrs.

Let B be the event that a wife will be alive after 20 yrs.

Now, PA = 0.8; PB = 0.9

PA = 1-PA = 1 - 0.8 = 0.2

PB 1 - PB = 1 - 0.9 = 0.1

Probability that both of them are alive = PA . PB = 0.8×0.9 = 0.72

Probability that none of them is alive = PA . PB = 0.2×0.1 = 0.02

Probability that at least one of them is alive = 1 - 0.02 = 0.08

Answer 2

Answer:

Let A be the event that a husband will be alive after 20 yrs.

Let B be the event that a wife will be alive after 20 yrs.

Now, PA = 0.8; PB = 0.9

PA = 1-PA = 1 - 0.8 = 0.2

PB 1 - PB = 1 - 0.9 = 0.1

Probability that both of them are alive = PA . PB = 0.8×0.9 = 0.72

Probability that none of them is alive = PA . PB = 0.2×0.1 = 0.02

Probability that at least one of them is alive = 1 - 0.02 = 0.08