Question

Becky bought a bag of mixed chocolates that have either a toffee or nut center. Her and four friends pulled out the first eleven and here they are in order: toffee, nut, toffee, toffee, toffee, toffee, nut, nut, toffee, toffee, toffee From what they have eaten so far, what are the odds the next one pulled has a toffee center? If there are 66 chocolates left in the bag, how many do you expect to have a nut center? What is the probability that the next 3 pulled do have a nut in the center?

Answer 1

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!!!