A new clothing store advertises that during its Grand Opening every customer tha
ID: 3218879 • Letter: A
Question
A new clothing store advertises that during its Grand Opening every customer that enters the store can throw a bouncy rubber cube onto a table that has squares labeled with discount amounts. The table is divided into ten regions. Five regions award a $10 discount, two regions award a $20 discount, two regions award a $30 discount, and the remaining region awards a $S0 discount. Use this information to answer problems 1-6. State your answers as a reduced fraction or a decimal What is the probability that a customer gets more than a $20 discount? What is the probability that a customer gets less than a $20 discount? What is the probability that the first two customers both get a $10 discount? What is the probability that none of the first three customers got a $30 discount? What is the probability that there is at least one customer to win a $50 discount among the first five customers that enter the store? As you enter the store you watch the four people in front of you all win $$0 discounts. The store manager tells you how lucky you are to be throwing the cube while it is on a hot streak, but the friend with you says you're unlucky because the streak can't continue. Is either the store manager or your friend correct? Explain.Explanation / Answer
Solution:-
1) The probability that costumer gets more than 20 discounts is 0.3.
The number of times person gets more than 20 discounts = 3
Total number of discounts = 10
The probability that costumer gets more than 20 discounts is 0.3.
2) The probability that costumer gets less than 20 discounts is 0.50.
The number of times person gets less than 20 discounts = 5
Total number of discounts = 10
The probability that costumer gets less than 20 discounts is 0.50
3) The probability that first two costumers gets 10 discounts is 0.25.
The probability of first costumer getting 10 discounts = 0.5
The probability that first two costumers gets 10 discounts = 0.5 × 0.5
The probability that first two costumers gets 10 discounts = 0.25.
4) The probability that none of first three costumer gets a 30 discounts is 0.512
The probability that first costumer will not get 30 discounts = 0.8
The probability that none of first three costumer gets a 30 discounts = 0.8 × 0.8 × 0.8
The probability that none of first three costumer gets a 30 discounts = 0.512
5) The probability that there is atleast one costumer to win $ 50 discount among first 5 costumers enters the store.
p = 0.10, n = 5
By applying binomial distribution:-
P(x, n, p) = nCx*p x *(1 - p)(n - x)
P(x > 1) = 0.4095
The probability that there is atleast one costumer to win $ 50 discount among first 5 costumers enters the store is 0.4095.
7) The probability of getting $ 50 discount is independent of previous throw, each time you will have probability of 0.10 to get the discount of $50. Neither the manager or the friend is correct.
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