RA 11: Probability of Survival Calculation

CFA Level III
#1

I know this is one of those things I should just memorize and move along but I’m curious why the joint probability of survival for a couple is being calculated as the difference between the sum of the individual probabilities of survial for each spouse less the product of the individual probabilities of survival for each spouse.

Pjoint survival= (Phusband + Pwife) - (Phusband * Pwife)

Shouldn’t it just be Phusband*Pwife; since it is a joint probability of mutually exclusive events? Is it perhaps just a more conservative approach to approximating joint survival?

I was never the best statstistics student, but this one has me puzzled.

#2

either husband survives or wife survives

which is husband survives + wife surives - both survive

#3

More explicitly:

Either husband survives or wife survives or both survive

P(A or B) = P(A) + P(B) − P(AB)

Level I junk.

#4

You are deducting the probability of joint survival so how can the probability reflects that both survices?

#5

joint survival = Either survives.

As S2000 mentioned above - it is Level 1 Junk - and you should not be asking this here.

It is the straight forward Venn diagram stuff.

#6

if the husbard dies before the wife is 60, there is a 50% the wife remarries, forfeiting the pension right… loads of scope for twisting this one round, so memorise it.

#7

If P(H) = 0.8 and P(E) = 0.7, then the probability is >1 ?

#8

Of course not.

At worst, P(H and E) = 0.5, so you’d get

P(H or E) = 0.8 + 0.7 − 0.5 = 1.0

More likely, P(H and E) > 0.5.

#9

That was a rhetorical question smiley

#10

This is exactly what i m saying. That this formula shows the probability of either husband or wife survice, this does not include probability for survival of both. Where as above its written both survice. Thanks anyways i just got confused with this statement so thought to clearify it :smiley:

#11

Aha!

You’re mistaken: it _ does _ include the probability that both survive.

P(H) is the probability that the husband survives, whether the wife survives or not, so the probability of both is included.

P(W) is the probability that the wife survives, whether the husband survives or not, so the probability of both is included.

Thus, P(H) + P(W) includes the probability that both survive _ twice _; we have to subtract P(HW) so that we count it only once.

#12

Ooooops :smiley: So since level 1 i was having the wrong concept it means ROFL…Thanks a lot for the wonderful concept. Got it right now