math II probability problem

Test Preparation SAT Subject Test Preparation
1

<p>Four letters mailed today each have a 2/3 probability of arriving in two days or sooner. What is the probability that exactly two of the four letters will arrive in two days or sooner?</p>

<p>The answer is 8/27 but I keep getting 16/27.</p>

<p>Here's how I tried to solve it:
4c2=6 so there are 6 ways to select 2 out of 4 letters</p>

<p>Probability of the first two to arrive in two days or sooner is 2/3<em>2/3</em>1/3<em>1/3=8/81
Any of those six combinations is equally probable so 6</em>8/81= 16/27</p>

<p>Anyone can explain me why am I wrong?</p>

2

<p>You have a computational mistake there, my friend. 2/3<em>2/3</em>1/3*1/3 does not equal 8/81, it equals 4/81, which gives the correct answer upon multiplication with the number of ways to select two out of four letters.</p>

3

<p>…and I spent about 20 minutes trying to figure out why my answer didn’t match…:confused:
thanks:)</p>