Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

A die is loaded to give the probabilities:

$$P(1)=0.3$$ $$P(2)=0.1$$ $$P(3)=0.15$$ $$P(4)=0.15$$ $$P(5)=0.15$$ $$P(6)=0.15$$

and thrown 8 times. Find the probability that both 1 and 2 occur.

This problem seems funnily easy but I can't see how to solve it without brute-forcing all the combinations...

share|improve this question

2 Answers 2

up vote 3 down vote accepted

Hint: You can use inclusion/exclusion. Calculate the chance that 1 doesn't occur, which is $0.7^8$ and the chance that 2 doesn't occur. Add them together, but you have double counted the cases where neither occurs, so deduct the chance which neither occurs.

share|improve this answer

It is easier to find the probability that $1$ or $2$ or both fail to occur.

share|improve this answer
    
Ah, misread "both fail." –  Thomas Andrews Apr 18 '13 at 20:49

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.