5. 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?
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
5. 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
(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?
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n1 = Number of ways in which 5 numbers can be drawn out of 70 numbers without replacement
n2= number of ways in which 1 number can be chosen out of 25 numbers.
n2 = 25
So, the probability that 5 correct number and 1 correct number chosen is given as follows:
Notice that P is near zero. I.e. very low.
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