Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

When a random experiment is conducted, the probability that [#permalink]
29 Jan 2010, 10:26

00:00

A

B

C

D

E

Difficulty:

5% (low)

Question Stats:

85% (01:52) correct
14% (01:07) wrong based on 14 sessions

When a random experiment is conducted, the probability that event A occurs is 1/3. If the random experiment is conducted 5 independent times, what is the probability that event A occurs exactly twice?

--------------------------------------------------------------------------------------- If you think you can,you can If you think you can't,you are right.

Last edited by Bunuel on 08 Jun 2012, 05:49, edited 2 times in total.

When a random experiment is conducted, the probability that event A occurs is ????. If the random experiment is conducted 5 independent times, what is the probability that event A occurs exactly twice?

You need to add information about the probability that even A occurs
_________________

Lets say getting A is represented by W and not getting A by L. prob of A = 3/10 prob of not getting A= 7/10 Out of 5 times, getting 2 As can be done in 5C2 = 10 ways.

So prob of getting 2 As = 10*3/10 * 3/10 * 7/10 * 7/10 * 7/10 = 3087 / 10000

.03087 * 10 = .3087 how ever this does not match any given options

You are right. There was a typo in the stem, 0.3 instead of 1/3. Typo edited. Thank you.

Complete solution: When a random experiment is conducted, the probability that event A occurs is 1/3. If the random experiment is conducted 5 independent times, what is the probability that event A occurs exactly twice? A. 5/243 B. 25/243 C. 64/243 D. 80/243 E. 16/17

The probability that event A occurs is \frac{1}{3}; The probability that event A will not occur is 1-\frac{1}{3}=\frac{2}{3}.

We want to calculate the probability of event YYNNN (Y-occurs, N-does not occur).

P(YYNNN)=\frac{5!}{2!3!}*(\frac{1}{3})^2*(\frac{2}{3})^3=\frac{80}{243}, we are multiplying by \frac{5!}{2!3!} as event YYNNN can happen in # of times: YYNNN, YNYNN, NNNYY, ... basically the # of permutations of 5 letters YYNNN out of which 2 Y's and 3 N's are identical (\frac{5!}{2!3!}).