# What if someone challenged you to never roll a 3? If you were to roll the dice 18 times, what would be the empirical probability of never getting a three? Percent Probability Solution (Roun...

1. What if someone challenged you to never roll a 3? If you were to roll the dice 18 times, what would be the empirical probability of never getting a three?
2.  Percent Probability Solution (Rounded to the Nearest Whole Percent) (2 points) ? Likelihood Scale Term (2 points) ?

We know that,

When a fair die with 6 sides is rolled once , the probability of getting a number from 0 to 6 is 1/6.

Therefore, when the given die is rolled once, the probability of getting a number 3 = 1/6

Thus , the probability of not getting a number 3 when the die is rolled once = 1- (1/6) = 5/6.

Now , when the same die is rolled 18 times , the probability of not getting a number '3' is given by ,

= (5/6)18 = 0.03756

= 0.04 (approx)

Thus , percent probability of not getting a number '3' = 0.04 × 100% = 4%

Further ,

the probability of getting a number '3' after 18 rolls = 1 - 0.03756

= 0.96244 = 0.96 (approx)

and the percent probability of getting a number '3" on 18 rolls = 0.96 × 100% = 96%

Likelihood scale term for the given event ( of not getting a number '3' on 18 rolls ) can be given by ,

It is unlikely to get a number 3 after a fair die with 6 sides is rolled 18 times.

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