• Mar 12th 2006, 10:20 AM
Jon
Delete
• Mar 12th 2006, 04:12 PM
ThePerfectHacker
Quote:

Originally Posted by Jon
need help ASAP Six dwarfs: Sleepy, Happy, Bashful, Doc, Grumpy, and Wishbone are available for a behavior experiment. In the experiment, 4 of therm are selcted and arranged in a row. Find the probability for the following events:

Doc is first
Wishbone is last
Bashful is first and Happy is last
Happy is first, Grumpy is second , Doc is thrid and Wishbone is last
Sleepy is first, second or third but not last
Wishbone is not selected

Doc is first:
He needs to be selected AND he would be the first. The probability that he is selected is $\displaystyle \frac{_5C_3\cdot _1C_1}{_6C_4}=\frac{2}{3}$
The probability that he is first is $\displaystyle 1/4$ thus, the answer is $\displaystyle \frac{1}{4}\cdot \frac{2}{3}=\frac{1}{6}$

Wishbone:
Same thing as in the first problem, same answer.

Bashful is first, Happy is last:First they need to be selected out of 6 people which is $\displaystyle \frac{_2C_2\cdot _4C_2}{_6C_4}=\frac{2}{5}$
Now bashful is first which is $\displaystyle 1/4$ and hapy is last which is $\displaystyle 1/3$ because only 3 poeple remain after bashful. Thus,
$\displaystyle \frac{2}{5}\cdot \frac{1}{4}\cdot \frac{1}{3}=\frac{1}{30}$

For the next problem, you need to select all 4 which is $\displaystyle \frac{_4C_4}{_6C_4}=\frac{1}{15}$, Now you need them is proper order which is for the first one $\displaystyle 1/4$ for the second $\displaystyle 1/3$ for the third $\displaystyle 1/2$ and for the last $\displaystyle 1/1$ Thus,
$\displaystyle \frac{1}{15}\cdot \frac{1}{4}\cdot \frac{1}{3}\cdot \frac{1}{2}\cdot \frac{1}{1}=\frac{1}{360}$

Sleepy Not last: Add that he is first or second or third. Which is $\displaystyle \frac{1}{6}$ as in the first problem. Thus, $\displaystyle \frac{1}{6}+\frac{1}{6}+\frac{1}{6}=\frac{1}{2}$

Wishbone not selected: If the probability of selecting him is $\displaystyle \frac{2}{3}$ then the probability of not selecting him is $\displaystyle \frac{1}{3}$
Hope this helps, and also that I did not erred.
• Mar 12th 2006, 04:18 PM
Jon
Thanks
I did come up with some of the answers, but on others I see where I made my mistake. :cool: Thanks.
• Mar 12th 2006, 06:10 PM
ThePerfectHacker
Quote:

Originally Posted by Jon
I did come up with some of the answers, but on others I see where I made my mistake. :cool: Thanks.

Welcome, no need to delete the post let other members see if there are any other ways of answering it or maybe they want to see the answer.