<p>X 0 0 X</p>
<p>The figure above represents four offices that will be assigned randomly to four employees, one employee per office. If Karen and Tina are two of the four employees, what is the probability that each will be assigned an office indicated with an X?</p>
<p>a. 1/16
b. 1/12
c. 1/6
d. 1/4
e. 1/2</p>
<p>Is the answer C?</p>
<p>is the answer c?
if so
there is a 2/4 chance to hit the X then there is a 1/3 chance to hit the X
so
0.5 x 1/3 = 1/6</p>
<p>Yes. The answer is C. Could you please elaborate on the solution?
Do I simply multiply the two probabilities?</p>
<p>first its X 0 0 X so there is a 2/4 chance to get X
after that you take out one X
so its 0 0 X
now there is a 1/3 chance
1/3x2/4 = 1/6</p>
<p>in probability, two things happening with “AND” means you multiply the probabilities of each event.</p>
<p>if it’s things happening with “OR”, you add the probabilities of the different events.</p>
<p>That’s weird. I knew to multiply 1/2 by 1/3… but there are two ways of this happening. So normally you would multiply by 2 and that would give you 1/3. can someone explain why multiplying by 2 is not applicable in this case?</p>
<p>we get 1/6 by mutiplying 2/4(Karen’s chance of getting an X) by 1/3 (Tina’s chance); in this case, 2 has already been used once(2*1/4=2/4), meaning we have included both cases for Karen.</p>
<p>The answer is C:</p>
<p>The probability of first girl getting assigned to X is 2/4
The probability of 2nd girl getting assigned to X AFTER first girl gets X is 1/3
Multiply those together, you get 2/12 = 1/6</p>
<p>The above solutions are really the best, quickest way. But if you are still not convinced, here is another way to think about it. </p>
<p>Say you have Karen, Tina and the other two people. Call them X and Y.</p>
<p>You could use 4! = 4 x 3 x 2 x 1 to find that there are 24 ways to assign the seats.</p>
<p>You could even list all the possibilities (but I won’t).</p>
<p>Then, list all the ways that have Karen and Tina on the ends:</p>
<p>K X Y T
K Y X T
T X Y K
T Y X K</p>
<p>As you see, 4 out of 24 ways = 1/6.</p>
<p>But the other way is still better.</p>
<p>so the offices are X O O X .
Karen’s chance at getting an office with an X is 2/4 .</p>
<p>Now it’s Tina’s turn. Karen already has an office with an X, so there are 3 offices left ( X O O ) and out of those three, only one of which has an X. So Tina has a 1/3 chance of getting the remaining X. </p>
<p>Now that we know each person’s chance of getting an X office. By simply doing (2/4)*(1/3)= (2/12)=(1/6). So C, (1/6) is the answer.</p>
<p>For a faster form of what pckeller did:
Total outcomes: 4 3 2 1 = 24 permutations.
Outcomes with success: 2 2 1 1 = 4 permutations.
If you’re wondering how I got 2 2 1 1, you fill in the blanks that are limited first. This means Karen or Tina must fill in the first blank (2). The remaining one must fill in the last blank (1). Then there’s two left for the other two blanks so it’s a successive 2 and then 1. This gives you four permutations possible.</p>
<p>Outcomes with success / total outcomes = answer
It takes about 10-15 seconds to get the answer from start to finish.</p>
<p>Thanks guys. This was really helpful. I think I’ve grasped the “essence” of these problems now.</p>