How do you do this problem and what are the conditions met that makes this a binomial distribution(all 3 conditions)?

The three conditions of a binomial distribution are:

In this case, all of the conditions of a binomial have been met because...

Since we only want one red chip, and there are 5 slots to fill (1 red+4 black), this must mean there are exactly 5 ways to get what we want.

We could have the following selections

With R = red and B = black. This value 5 will be used as the binomial coefficient. You can find this value through the use of the nCr combination formula or using Pascal's Triangle.

Note: we only have 3 black chips, but because we put the chip back each time, it means we can get more than 3 black selections.

We'll also be using x = 1 to find the probability of getting exactly one red chip

P(x) = (binomialCoefficient)*(p)^x*(1-p)^(n-x)

P(x) = 5*(p)^x*(1-p)^(n-x)

P(1) = 5*(2/3)^1*(1-2/3)^(5-1)

P(1) = 0.0411523

The probability of getting exactly one red chip is roughly 0.0411523

yes

step-by-step explanation: