Answer:
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
<u><em>Let X = Number of sixes on a die</em></u>
So, X ~ Binom(n = 6, p = 0.20)
Now, Probability of rolling at least 4 sixes is given by = P(X  4)
 4)
P(X  4) = P(X = 4) + P(X = 5) + P(X = 6)
 4) = P(X = 4) + P(X = 5) + P(X = 6) 
=  
=  
=  0.0154 + 0.00154 + 0.000064 
=  0.01696
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Therefore, probability of rolling at least 4 sixes is 0.01696.