A single die is rolled 7 times. What is the probability that a six is rolled exactly once, if it is known that at least one six is rolled?

Question

Can you show the steps to help me understand?

Answer 1

Total possible rolls = 6 x 6 x 6 x 6 x 6 x 6 x 6 = 279936

Number with no sixes rolled = 5 x 5 x 5 x 5 x 5 x 5 x 5 = 78125

Number with at least one six rolled = 279936 - 78125 = 201811

So out of these, how many ways can a six be rolled exactly once ??

Well we can choose the die that got a six in 7 ways.

The other six dice can be rolled in 5 x 5 x 5 x 5 x 5 x 5 = 15625 ways

So the number of ways = 7 x 15625 = 109375

So required probability = 109375 / 201811 = 0.54