If you select 3 letters (with replacement) from the word MATHEMATICAL, what is the probability of getting two 'M's.
-
$\begingroup$ Thanks for the answers. I get 5/72 as well. But the correct answer is 11/144. Could some one please explain this answer to me. Thx. $\endgroup$– SusieAug 25, 2014 at 11:08
-
2$\begingroup$ I do not agree with the answer of 11 / 144. $\endgroup$– bobbymAug 25, 2014 at 11:12
-
$\begingroup$ I tend to agree with you. But the answer in the text book is 11/144 $\endgroup$– SusieAug 25, 2014 at 11:16
-
1$\begingroup$ The textbook's answer is wrong. $\endgroup$– David MitraAug 25, 2014 at 11:21
-
$\begingroup$ Much appreciated. Thank you. $\endgroup$– SusieAug 25, 2014 at 11:24
3 Answers
How many letters are there in the word MATHEMATICAL? $12$
How many letters are $M$ here? $2$
We want the probability of getting two 'M's takes considering all three cases. When we get a non-M on the first, second or third pick.
$\frac{10}{12}*\frac{2}{12}*\frac{2}{12}+\frac{2}{12}*\frac{10}{12}*\frac{2}{12}+\frac{2}{12}*\frac{2}{12}*\frac{10}{12}=30*\frac{2^2}{12^3}=\frac{5}{72}$
The number of M's obtained is binomially distributed with $p={1\over6}$. The probability to obtain exactly two M's in three draws is therefore given by $${3\choose 2}\ \left({1\over6}\right)^2\ \left({5\over6}\right)^1={5\over72}\ .$$
I am getting,
$$3\left ( \frac{2}{12}\right )\left ( \frac{2}{12}\right )\left ( \frac{10}{12}\right )=\frac{5}{72}$$
-
$\begingroup$ Why do we have three answers? What is wrong with my method and/or $8\pi \mathrm{r}$'s? $\endgroup$– TonyAug 25, 2014 at 11:05
-
$\begingroup$ I think because I am treating (m,m,X) as different than (X,m,m) and (m,X,m). $\endgroup$– bobbymAug 25, 2014 at 11:09
-
-
$\begingroup$ I am your upvote here, and I have no idea why I got one more upvote than you, considering my answer was obtained from your help! $\endgroup$– TonyAug 26, 2014 at 14:42
-
$\begingroup$ It us not a big deal, glad you got them. Looks like they are closing the question anyway. $\endgroup$– bobbymAug 26, 2014 at 15:08