what are the theorems on probability?

Question

a survey in a certain locality reveals that the probability of a man dying after the age of 0.6 and the probability of a woman dying after the age of 60 is 0.5. if a couple comes from this locality, what is the probability that:

a) both will die before the age of 60?

b) either will die after 60?

Answer 1

PROBLEM A:

P(man dies before 60) = 1 - 0.6 = 0.4
P(woman dies before 60) = 1 - 0.5 = 0.5

P(both die before 60) = 0.4 x 0.5 = 0.2 = 20%

PROBLEM B:

Either will die after 60 is the opposite of both dying before 60.

P(either (or both) die after 60) = 1 - P(both die before 60)
= 1 - 0.20 = 0.80 = 80%

Answer 2

1

Let M be the event that a male dies before age 60
Let F be the event that a female dies before age 60

P(M) = 1 -0.6 = 0.4
P(F) = 1 - 0.5 = 0.5

Assuming that the events M and F are independent then we simply need to multiply the individual probabilities to find the intersection

P( M ∩ F ) = P(M) * P(F) = 0.4 * 0.5 = 0.2

---- ---- ---- -----

2
For any two events A and B

P(A U B) = P(A) + P(B) - P(A ∩ B)

if we let A be the event the male dies after age 60
Let B be the event that the female dies after age 60, then

P(A U B) = 0.6 + 0.5 - 0.6 * 0.5 = 0.8

Answer 3

qa
1/5

qb
1/2