Approach for a type of Probability q

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gmatdriller: Master | Next Rank: 500 Posts; Posts: 418; Joined: Sun Jul 04, 2010 12:48 pmFollowed by: 3 members; Thanked: 6 times

by gmatdriller » Sat Jul 04, 2015 8:57 pm

Pls explain where to apply the formula below:

Solution = P(A)*P(NOT B) + P(NOT A)*P(B)
I'll be glad to have a good example.

Is this one a good example?
A student takes 2 tests on Biology & Maths;
What is the chance that he passes only one subject?

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Source: Beat The GMAT — Problem Solving | Sat Jul 04, 2015 8:57 pm

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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Sun Jul 05, 2015 9:12 am

Hi gmatdriller,

The formula you've listed is for situations in which there are two events, each with two possible outcomes AND the question asks for the probability that JUST ONE of the events occurs.

Your example matches this concept perfectly.

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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gmatdriller: Master | Next Rank: 500 Posts; Posts: 418; Joined: Sun Jul 04, 2010 12:48 pmFollowed by: 3 members; Thanked: 6 times

by gmatdriller » Tue Jul 07, 2015 11:56 am

[email protected] wrote:Hi gmatdriller,

The formula you've listed is for situations in which there are two events, each with two possible outcomes AND the question asks for the probability that JUST ONE of the events occurs.

Your example matches this concept perfectly.

GMAT assassins aren't born, they're made,
Rich

Thanks for the response, Rich.

Kindly help with standard questions that considers such criteria.

Thanks

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seandcarey: Newbie | Next Rank: 10 Posts; Posts: 6; Joined: Tue Jul 07, 2015 11:41 am

by seandcarey » Tue Jul 07, 2015 12:48 pm

If you didn't want to be bothersome in remembering formulas, you can think of it like a sample space.

Using your example, lets say that she has a 60% of passing biology, and 70% chance of passing math.

What is the probability that she passes both subjects?
.7 * .6 = .42 = 42% she passes both

What is the probability that she passes neither subject?
(1 - .7) * (1 - .6) - .12 = 12%

What is the probability she passes only one of the subjects?
1 - (.42 + .12) = .46 = 46% for a sample space of 1.

If we used the formula you provided, you'd get the same answer.

.7 * .4 + .6 * .3 = .46

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