An unbalanced die is manufactured so that there is a 20% chance of rolling a “six." The die is rolled 6
times. What is the probability of rolling at least 4 sixes?

Probability of rolling at least 4 sixes is 0.01696.

Step-by-step explanation:

We are given that an unbalanced die is manufactured so that there is a 20% chance of rolling a “six." The die is rolled 6  times.

The above situation can be represented through binomial distribution;

where, n = number trials (samples) taken = 6 trials

            r = number of success = at least 4

           p = probability of success which in our question is probability of

                 rolling a “six", i.e; p = 0.20

Let X = Number of sixes on a die

So, X ~ Binom(n = 6, p = 0.20)

Now, Probability of rolling at least 4 sixes is given by = P(X 4)

P(X 4) = P(X = 4) + P(X = 5) + P(X = 6)

=  

=  

=  0.0154 + 0.00154 + 0.000064

=  0.01696

Therefore, probability of rolling at least 4 sixes is 0.01696.

the entire expression should be subtracted from 30. to subtract the quantity, distribute the negative sign, which changes the signs on the terms. so, the –2 changes to positive and gets added to 30 instead of subtracted from it.

hope this ! ^w^

i think asking google will you get the answer to that question