Probability problem

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mjjking: Master | Next Rank: 500 Posts; Posts: 353; Joined: Sat Jan 20, 2007 1:29 am; Location: Italy; Thanked: 7 times; GMAT Score:720

Probability problem

by mjjking » Wed Nov 25, 2009 11:10 am

Hi folks,

one problem for you. How do you solve this?

Event A: probability 2/3
Event B: Probability 2/3
Event C: Probability 2/3
Event D: Probability 1/3

What is the probability that none of the events listed above occur?

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Source: Beat The GMAT — Problem Solving | Wed Nov 25, 2009 11:10 am

Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pm; Location: Toronto; Thanked: 1710 times; Followed by:614 members; GMAT Score:800

by Stuart@KaplanGMAT » Wed Nov 25, 2009 3:29 pm

mjjking wrote:Hi folks,

one problem for you. How do you solve this?

Event A: probability 2/3
Event B: Probability 2/3
Event C: Probability 2/3
Event D: Probability 1/3

What is the probability that none of the events listed above occur?

To solve this, we need more information. Let me rephrase the question that I think you meant to ask:

If the chart above shows the probability of independent events A, B, C and D occuring, what's the probability that none of the 4 events occurs?

If we want to know the probability of MULTIPLE independent events occuring (or not occuring), we MULTIPLY the individual probabilties.

Let's start by calculating the probability of each event NOT occuring using the handy "1 minus" formula:

Prob (event occuring) + Prob (event not occuring) = 1

or

1 - Prob (event occuring) = Prob (event not occuring)

So, the probability of each event NOT occuring:

Event A: 1 - 2/3 = 1/3
Event B: 1 - 2/3 = 1/3
Event C: 1 - 2/3 = 1/3
Event D: 1 - 1/3 = 2/3

And the probability of ALL 4 events NOT occuring is:

1/3 * 1/3 * 1/3 * 2/3 = 2/81