The Mega Millions game consists of drawing five numbers from the integers 1,2,3,…,70 (without replacement). Then a special number, a sixth number, is selected from a new set of umbers 1,2,3,…,25. A winning player must have selected the correct five numbers from the first set and the correct number from the second set. You get one set of six numbers for a $2 bet. You have already found the probability of winning the Mega Millions game if you make a $2 bet in a previous assignment. Now, please assume that $1.2 billion is wagered (i.e., 600 million tickets are purchased). (a) What is the probability that there will be no winners? (b) What is the probability there will be exactly one winner? (c) What is the probability that there will be two or more winners? (d) What is the expected number of winners? (e) What is the median number of winners? (f) What is the modal number of winners?
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
The Mega Millions game consists of drawing five numbers from the integers 1,2,3,…,70 (without replacement). Then a special number, a sixth number, is selected from a new set of umbers 1,2,3,…,25. A winning player must have selected the correct five numbers from the first set and the correct number from the second set. You get one set of six numbers for a $2 bet. You have already found the probability of winning the Mega Millions game if you make a $2 bet in a previous assignment. Now, please assume that $1.2 billion is wagered (i.e., 600 million tickets are purchased).
(a) What is the probability that there will be no winners?
(b) What is the probability there will be exactly one winner?
(c) What is the probability that there will be two or more winners?
(d) What is the expected number of winners?
(e) What is the
(f) What is the modal number of winners?
Note: Please just answer questions d,e, and f. Questions a,b, and c were answered previously.
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