CONVERT THE BELOW R CODE TO GRAPHICAL CODE AND INSPECT THE JOINS IN THEM

This is a binomial distribution problem, where the probability of rolling a 1 is 0.1 and the probability of not rolling a 1 is 0.9.

To find the probability of rolling twenty or fewer 1's, we can use the cumulative probability function of the binomial distribution:

P(X 20) = n=0^20 (n choose k) * p^k * (1-p)^(n-k)

where n is the number of rolls, k is the number of 1's rolled, p is the probability of rolling a 1, and (n choose k) is the binomial coefficient.

We want to find the number of rolls, n, that gives us a probability of 5% or less:

P(X 20) 0.05

We can solve this equation by using a binomial distribution calculator or a spreadsheet program. For example, using Excel's BINOM.DIST function, we can find that the number of rolls required is 99.

Therefore, if the experimenter rolls the die 99 times, the probability of rolling twenty or fewer 1's is about 5% or less.