Question

At least how many time do you have to roll a fair die to be sure that probability of rolling at least one 6 is greater than 9 in 10 (0.9)?

Answer 1

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Answer is 13.

Let that be n number of times.

When rolled n times, (5/6)^n is probability that 6 won't come up

1- (5/6)^n > .9

So, 1-.9 > (5/6)^n

.1 > (5/6)^n

Both sides, applying natural Log,

Ln(.1) > n*Ln (5/6)

n> 12.65 so, 13 times. ( sign of > reverses when -ive number is multiplied both the sides)

So, dice must be rolled atleast 13 times to be sure that probability of rolling at least one 6 is greater than 9 in 10 (0.9)