Probability

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krishna kumar: Junior | Next Rank: 30 Posts; Posts: 15; Joined: Fri Jun 11, 2010 10:02 pmFollowed by: 1 member

by krishna kumar » Fri Mar 04, 2011 9:15 pm

Hi ,

Could someone please help me to understand this problem.

If Event A and Event B are independent, is the probability that both Event A and Event B will happen greater than 0.3 ?

1. Probability that A will happen is 0.25

2. Probability that B will not happen is 0.71.

Thanks in advance.

OA D

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Source: Beat The GMAT — Data Sufficiency | Fri Mar 04, 2011 9:15 pm

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Fri Mar 04, 2011 10:11 pm

krishna kumar wrote:If Event A and Event B are independent, is the probability that both Event A and Event B will happen greater than 0.3 ?

1. Probability that A will happen is 0.25
2. Probability that B will not happen is 0.71

If two events are independent, then probability of happening both the events together is equal to the product of their individual probability. Also remember that individual probability of any event lies between 0 and 1.

Statement 1: Probability that A will happen is 0.25
Implies, P(A) = 0.25
As P(B) is less than or equal to 1, P(A)*P(B) â‰¤ 0.25 < 0.30

Sufficient

Statement 2: Probability that B will not happen is 0.71
Implies, P(B) = 0.29
As P(A) is less than or equal to 1, P(A)*P(B) â‰¤ 0.29 < 0.30

Sufficient

The correct answer is D.

Last edited by Anurag@Gurome on Fri Mar 04, 2011 11:20 pm, edited 1 time in total.

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navami: Legendary Member; Posts: 540; Joined: Sat Dec 20, 2008 7:24 pmFollowed by: 6 members; Thanked: 37 times

by navami » Fri Mar 04, 2011 10:17 pm

let probablity of A to happen is "a"
and probability of B to happen is "b"

for two independent events A and B to happen together, probabilty is = a*b

now, we have to find if a*b>0.3

1. given a=0.25, max value of b can be, bmax=1, hence a*bmax=.25 < 0.3,
hence option 1 is sufficient to answer the ques.

2. given b=1-0.71=0.29, max value of a can be, amax=1, hence amax*b=0.29< 0.3
hence option 2 is sufficient to answer the ques.

Hence D is the answer: Both options are independently sufficient to answer the question

This time no looking back!!!
Navami

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krishna kumar: Junior | Next Rank: 30 Posts; Posts: 15; Joined: Fri Jun 11, 2010 10:02 pmFollowed by: 1 member

by krishna kumar » Fri Mar 04, 2011 10:46 pm

thanks a lot.

So can we generalize this by saying

If we have 'n' independent events the probability that all of them happening will be less than the least of the 'n' individual probabilities.

thanks

krishna

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Fri Mar 04, 2011 10:56 pm

krishna kumar wrote:Hi ,

Could someone please help me to understand this problem.

If Event A and Event B are independent, is the probability that both Event A and Event B will happen greater than 0.3 ?

1. Probability that A will happen is 0.25

2. Probability that B will not happen is 0.71.

Thanks in advance.

OA D

What a question!

Here, since Event A and Event B are independent, hence the probability that both Event A and Event B will happen P (A and B)

= Probability that A will happen P (A) Ã— Probability that B will happen P (B)

We know that 0 â‰¤ P (A) or P (B) â‰¤ 1

(1) If P (A) = 0.25, then even the greatest possible value of P (B) [i.e. P (B) = 1] would keep P (A) Ã— P (B) always less than 0.3; thus answering a perfect NO to the stem. Sufficient

(2) Please note that P (B) = 1 - Probability that B will not happen = 1 - 0.71 = 0.29, now again, even the greatest possible value of P (A) [i.e. P (A) = 1] would keep P (A) Ã— P (B) always less than 0.3; thus answering a perfect NO to the stem. Sufficient

[spoiler]D[/spoiler]

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