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.

b. would be the answer : )

step-by-step explanation:

step 1: add -16x to both sides.

16x−4y+−16x=64+−16x  

−4y=−16x+64

step 2: divide both sides by -4.

−4y /-4 = -16x + 64/-4

answer:   y=4x−16

hope i'm right