logo

Ask Questions, Get Answers

 
X
 Search
Want to ask us a question? Click here
Browse Questions
Ad
Home  >>  CBSE XII  >>  Math  >>  Probability
0 votes

A die is thrown again and again until three sixes are obtained. Find the probability of obtaining the third six in the sixth throw of the die.

Can you answer this question?
 
 

1 Answer

0 votes
Toolbox:
  • A random variable $X$ following binomial distribution with parameter n and p its probability of 'r' succeses $\rightarrow$ $p(X=r)=C^{n}_{r} p^{r} q^{n-r}$, where p is probability of success and $q=1-p$ and $r=0,1,\dots,n$
We need to find the P (obtaining the third six in 6th throw of the die) = P (2 sixes in first 5 throws) + P (1 six in sixth throw)
Since P (getting a six) = $\large\frac{1}{6} \rightarrow$$ P (\text{obtaining the third six in 6th throw of the die}) = P (\text{2 sixes in first 5 throws}) \times \large\frac{1}{6}$
P (getting 2 sixes in first 5 throws) $= C^{5}_{2} \large\frac{1}{6}^{2} \large\frac{5}{6}^{5-2} = \frac{5 \times 4}{1 \times 2} \frac{5^3}{6^5} = \frac{625}{3888}$
$P (\text{obtaining the third six in 6th throw of the die}) = \large \frac{625}{3888} \times \frac{1}{6} = \frac{625}{23328}$
answered Mar 13, 2013 by poojasapani_1
edited Jun 22, 2013 by balaji.thirumalai
 

Related questions

Ask Question
student study plans
x
JEE MAIN, CBSE, NEET Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App
...