hemanthp wrote:

When a random experiment is conducted, the probability that event A occurs is

\frac{1}{3}. If the random experiment is conducted 5 independent times, what is the probability that event A occurs exactly twice?

5/243

25/243

64/243

80/243

16/17

took more time than I hoped for in the tests (

Kaplan). Don't forget to KUDOS if you like the question.

Tx.

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!}).

Answer: D.

Hope it's clear.