PLEASE HELP I DON'T KNOW WHAT TO DO D':
I don't understand what to do or how to even start....
In the town of Niceville, a local lottery is held once a year for the residents. Lottery tickets cost 50 cents apiece. Each lottery ticket contains four numbers, from 1 to 20. The lottery machine will select six numbers from 1 to 20. A winning ticket, worth $100, will contain four of the six numbers chosen by the machine.
a)How much money would a person need to spend to buy every possible combination of four numbers?
b)What is the probability, to the nearest ten-thousandth, that a person will select four correct numbers?
c)To the nearest ten-thousadnth, what is the probability that a ticket has NO correct numbers?
To solve these questions, we need to analyze the given information and use some basic concepts of probability.
a) To calculate the amount of money a person would need to spend to buy every possible combination of four numbers, we need to determine the number of possible combinations of four numbers that can be chosen from a set of six numbers. This can be calculated using the combination formula:
nCr = n! / (r!(n-r)!)
Here, n represents the total number of elements, and r represents the number of elements to be chosen. Using this formula, we can determine the number of combinations:
nCr = 6! / (4!(6-4)!), where n = 6 and r = 4
Simplifying the equation, we get:
6! = 6 x 5 x 4!
nCr = 6 x 5 x 4! / (4! x 2!)
Simplifying further, the factorials cancel out:
nCr = 6 x 5 / 2! = 15
So, there are 15 possible combinations of four numbers that can be chosen from a set of six numbers.
Now, since each combination costs 50 cents, to buy every possible combination, we multiply the number of combinations by the cost of each ticket:
Total cost = 15 x 0.50 = $7.50
Therefore, a person would need to spend $7.50 to buy every possible combination of four numbers.
b) To calculate the probability of selecting four correct numbers, we need to determine the total number of possible outcomes and the number of favorable outcomes.
The total number of possible outcomes is the number of combinations of six numbers that the machine can select: 6C6 = 1 (there is only one way to choose 6 numbers from a set of 6).
The number of favorable outcomes is the number of combinations of four numbers that can be matched with the winning combination of the machine. We already calculated this to be 15.
The probability can be calculated as:
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 15 / 1 = 15
Since probability is always between 0 and 1, to get the probability to the nearest ten-thousandth, we need to divide by the total number of possible outcomes multiplied by 10,000:
Probability = 15 / (1 x 10,000) = 0.0015
Therefore, the probability, to the nearest ten-thousandth, that a person will select four correct numbers is 0.0015.
c) To calculate the probability that a ticket has no correct numbers, we need to determine the number of unfavorable outcomes, which is the number of combinations of four numbers that do not match any of the six numbers chosen by the machine.
To calculate this, we need to subtract the number of favorable outcomes (15) from the total number of possible outcomes (6C4). We have already calculated 6C4 to be 15 previously.
Number of unfavorable outcomes = Total number of possible outcomes - Number of favorable outcomes
Number of unfavorable outcomes = 15 - 15 = 0
Since there are no unfavorable outcomes in this case, the probability of a ticket having no correct numbers is 0.
Therefore, the probability, to the nearest ten-thousandth, that a ticket has no correct numbers is 0.