A die is rolled 12 times Find the probability of rolling no more than 4 twos

 

A die is rolled 12 times Find the probability of rolling no more than 4 twos

 

Each roll is an independent event. So this is binomial probability.

You have to work out the prob of 

0 rolls of 2

1 rolls of 2

2rolls of 2

3 rolls of 2

4 rolls of 2

add then all together and subtract the answer from 1.

 

P(0 rolls of 2)=  \((\frac{5}{6})^{12}\)

 

P(1 rolls of 2)=  \( \binom{12}{1}(\frac{1}{6})^1(\frac{5}{6})^{11}\)

 

P(2rolls of 2)=  etc

 

P(3 rolls of 2)=

 

P(4 rolls of 2)=

 

etc