When Tim Hortons used physical cups for their Roll up the Ri

Ikunupe6v

Ikunupe6v

Answered question

2021-12-14

When Tim Hortons used physical cups for their Roll up the Rim contest (before switching over to "digital cups") they printed the cups so that 1 out of every 6 cups would be a winner. If the winning cups are truly randomly spread throughout the country.
a) A person feels they are particularly unlucky when it came to buying Tim Hortons coffee and winning Roll up the Rim. They often tell the story about how they kept buying losing coffee cups until the 16th cup was their first winning cup. What is the probability that someone could purchase this many cups and only win on the 16th cup?

Answer & Explanation

Mary Herrera

Mary Herrera

Beginner2021-12-15Added 37 answers

Step 1
Random variables are of 2 types, discrete and continuous. A discrete random variable can only take countable and finite number of possible values. A continuous random variable can take infinitely and uncountably many possible values.
Based on these classification of random variables, the probability distributions are divided in to 2, discrete and continuous. Geometric distribution is a discrete probability distribution.
Step 2
The geometric distribution indicates the number of failures before the first success (in Bernoulli trials). Here the probability of winning is p=160.167. (indicates that one of every 6 cup will be a winner). Let X be a geometric random variable that indicates that indicates the number of cup purchase needed to get the first win. The probability mass function of binomial distribution is given below.
P(X=x)=(1p)x1(p)
Here probability that someone have to purchase 16 cups and only win on the 16th cup has to be calculated. This indicates P(X=16). This can be calculated in the following way.
P(X=16)=(10.167)161(0.167)
=0.83315(0.167)
=0.011
Thus 0.011 is the required probability.
movingsupplyw1

movingsupplyw1

Beginner2021-12-16Added 30 answers

Step 1
Find the expected number of cups that are needed to buy until finding a winning cup:
Given that 1 out of every 6 cups is a winner.
Consider the event that winning a cup as a “success”. It is known that the the probability of success in each trial is p=16=0.1667
Consider X as the number of trials until finding a winning cup. Then, X is a Geometric distribution with parameters (p=0.1667)
The expected number of cups that are needed to buy until finding a winning cup is obtained as 6 from the calculation given below:
E(X)=1p
=10.1667
=6S
Thus, the expected number of cups that are needed to buy until finding a winning cup is 6.

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