3
$\begingroup$

If you select 3 letters (with replacement) from the word MATHEMATICAL, what is the probability of getting two 'M's.

$\endgroup$
5
  • $\begingroup$ 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. $\endgroup$
    – Susie
    Aug 25, 2014 at 11:08
  • 2
    $\begingroup$ I do not agree with the answer of 11 / 144. $\endgroup$
    – bobbym
    Aug 25, 2014 at 11:12
  • $\begingroup$ I tend to agree with you. But the answer in the text book is 11/144 $\endgroup$
    – Susie
    Aug 25, 2014 at 11:16
  • 1
    $\begingroup$ The textbook's answer is wrong. $\endgroup$
    – David Mitra
    Aug 25, 2014 at 11:21
  • $\begingroup$ Much appreciated. Thank you. $\endgroup$
    – Susie
    Aug 25, 2014 at 11:24

3 Answers 3

Reset to default
3
$\begingroup$

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.

$\frac{10}{12}*\frac{2}{12}*\frac{2}{12}+\frac{2}{12}*\frac{10}{12}*\frac{2}{12}+\frac{2}{12}*\frac{2}{12}*\frac{10}{12}=30*\frac{2^2}{12^3}=\frac{5}{72}$

$\endgroup$
0
3
$\begingroup$

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 $${3\choose 2}\ \left({1\over6}\right)^2\ \left({5\over6}\right)^1={5\over72}\ .$$

$\endgroup$
2
$\begingroup$

I am getting,

$$3\left ( \frac{2}{12}\right )\left ( \frac{2}{12}\right )\left ( \frac{10}{12}\right )=\frac{5}{72}$$

$\endgroup$
5
  • $\begingroup$ Why do we have three answers? What is wrong with my method and/or $8\pi \mathrm{r}$'s? $\endgroup$
    – Tony
    Aug 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). $\endgroup$
    – bobbym
    Aug 25, 2014 at 11:09
  • $\begingroup$ Oh good point, thank you for that! $\endgroup$
    – Tony
    Aug 25, 2014 at 11:10
  • $\begingroup$ 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! $\endgroup$
    – Tony
    Aug 26, 2014 at 14:42
  • $\begingroup$ It us not a big deal, glad you got them. Looks like they are closing the question anyway. $\endgroup$
    – bobbym
    Aug 26, 2014 at 15:08

Not the answer you're looking for? Browse other questions tagged .