A fair die is thrown 10 times. What is the probability of rolling a 1 on exactly 2 of the 10 throws?

Question

A fair die is thrown 10 times. What is the probability of rolling a 1 on exactly 2 of the 10 throws?

 

Please help!!

Answer 1

The probability that you roll a 1 on a single die is 1/6 for each roll.

 

So if you want exactly 2 occurrences, that would be (1/6)² * (5/6)⁸ . That's a 1 twice and something else 8 times to make up all ten rolls.

 

But we're not done. The 1 could have been on the first two rolls, the last two rolls, the third and fifth roll....we don't know.

 

That's why you need to multiply this answer by ₁₀C₂, (I hope you know this notation) which equals (10*9)/(2*1)=45.

 

So your answer is 45*(1/6)²*(5/6)⁸ = .2907 or approximately 29%of the time.

 

Hope this helped.