* P(A and B) = P(A) . P(B)

[rte.sushil]

Question:
79% of US people aged 30 had health insurance in 1999. A person who was 39 in 2008 had an 80% chance of having health insurance.

Assuming independent probabilities in each year, the probability that a U.S. citizen who was 30 in 1999 had health insurance both in 1999 and in 2008 is between:

Solution:
The probability we want is 79% × 80%.

0.79 × 0.80 = 0.632 = 63.2%

Query:

I am lost why these 2 probabilities are multipled?
Usually we multiple in scenarios as:
Example:
Suppose we have two dice. A is the event that 4 shows on the first die, and B is the event that 4 shows on the second die. If both dice are rolled at once, what is the probability that two 4s occur?
P(A) = 1/6
P(B) = 1/6
P(A and B) = P(A) . P(B) = 1/6 . 1/6 = 1/36

I am not able to compare concept of the question with the example. Please suggest.

[RonPurewal]

what's the source of this problem? i don't see this problem in our database, so i don't think it's ours.

(this looks like a problem from someone's high-school Algebra II textbook; it doesn't look anything like the probability problems that show up on the gmat.)

please verify the source of this problem within the next few days.

* if it's actually from a MGMAT CAT exam, please give the test #, problem #, and the title given to the problem (visible in the list of quant problems when you review the test).

* if it isn't, then this thread doesn't belong here -- please start a new thread in the correct folder, with an explicit citation of the source.

thanks.

[rte.sushil]

ofcourse this problem is from Manhtattan GMAT test series from IR test.
i can't upload picture and the IR question had a graph. so i took out the doubt part.

[jlucero]

Note: I have this question over to the IR section for you, but in the future please post questions to the proper forum.

To answer your question, yes, we should be multiplying probabilities here since these are independent events. In the real world, we might assume that someone who has insurance in 2000 is going to be more likely to have insurance in 2001. But in the GMAT world, we can't assume these things and in fact, the question is prefaced with "Assuming independent probabilities in each year". We can assume that having health insurance in 1999 and 2008 are as independent as two separate rolls of a dice.