M&M Probability Time to open another 1.69 ounce pack of M&M\'s. Rip open a corne
ID: 3200594 • Letter: M
Question
M&M Probability
Time to open another 1.69 ounce pack of M&M's. Rip open a corner but don't pour them out this time. You are going to pour our several samples. The focus here is on the Blue candies. Approximately 1 out of every 4 in both the plain and peanut M&M's are blue.
1st sample) Pour out 4 candies. (1) Count and record the total blues. Probability dictates that there should be 1 blue, but in a small sample anything can happen, and the results are random.
2nd sample) Pour out 8 candies. (2) Count and record the total blues. Probability dictates that there should be 2 blues, but we shall see.
3rd sample) Pour out 12 candies. (3) Count and record the total blues. Probability dictates that there should be 3 blues, and you are probably wondering why you are counting instead of eating.
4th sample) Pour out 16 candies. (4) Count and record the total blues. Probability dictates that there should be 4 blues, and you can't believe you are holding so many delicious candies in your hand at once.
5th sample) There should be anywhere from 13 to 17 candies left in the package, so tell me (5a) how many were left and (5b) how many of them were blue.
Total package) Add up your totals. (6a) How many candies were in the package and (6b)how many of them were blue. How close was it to one-fourth of the package? Were each of the samples consistent or did they vary a bunch?
Explanation / Answer
Solution :-
1st sample) Pour out 4 candies.
P (Blue) = 1/4
2nd sample) Pour out 8 candies
P (Blue) = 2/8 = 1/4
3rd sample) Pour out 12 candies.
P (Blue) = 3/12 = 1/4
4th sample) Pour out 16 candies.
P (Blue) = 4/16 = 1/4
5th sample) There should be anywhere from 13 to 17 candies left in the package
(5a) how many were left - 17 (As the total number of M&M should be 57.)
(5b) how many of them were blue - approximately 4 should be blue
Total package) Add up your totals.
(6a) How many candies were in the package - 57 candies
(6b)how many of them were blue - approximately 14
How close was it to one-fourth of the package?
As 1/4 of 17 is 4.25. Therefore out of a pack of 57, if 14 are blue, i.e., 14/57 are blue or if we simplify, we get 1/4.07 = 0.2457 as the probability of M&Ms that are blue in the pack. This is really close to one-forth or 0.25 of the probability of blue candies in the package. which was the claimed statement.
The samples were consistent and did not vary significantly.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.