Answer
Part A
Probability that the next chocolate will have a toffee center = (8/11)
Part B
Expected number of chocolates with nut centers = 18 nut centers
Part C
Probability of the picking three consecutive chocolates with nut centers
= (27/1331)
= 0.0203
Explanation
The first 11 chocolates had 8 toffee and 3 nut centers.
The result from these first 11 picks will be used to calculate the rest of the probability or make predictions.
So, for the first part of the question.
Probability that the next chocolate will have a toffee center
= (8/11)
Part B
If there are 66 chocolates left in the bag, how many do you expect to have a nut center?
Probability of picking a chocolate with nut center = p = (3/11)
Number of chocolates in total = n = 66
Expected number of chocolates with nut centers
= np
= (66) (3/11)
= 18 nut centers
Part C
What is the probability that the next 3 pulled do have a nut in the center?
Probability of picking a chocolate with nut center = (3/11)
Probability of the picking three consecutive chocolates with nut centers
= (3/11) × (3/11) × (3/11)
= (27/1331)
= 0.0203
Hope this Helps!!!
