Part A
Use the binomial probability distribution formula.
p = 0.54 = probability of getting a purple marble
n = 5 = sample size
x = 2 = number of purple we want to get
The portion is from the nCr combination formula. The exclamation marks indicate a factorial.
Alternatively, you could use Pascal's Triangle for that portion.
<h3>Answer: 0.283831776</h3>This decimal value is exact. Round it however you need to.
============================================================
Part B
To find the expected value, aka the mean, we multiply the sample size and probability of getting a purple marble on any single selection.
n*p = 5*0.54 = 2.7
<h3>Answer: 2.7</h3>