1) A lottery draws six numbers from 42 possibilities, without regard to order. What is the total number of possible results of the drawing.
In the lottery from the before, what is the probability that you pick the winnin number?
In the Lottery from number 1, you pay the state of cailfornia 1 dollar for a ticket. If you pick the winning number, your state pays 10,000,000. What is the expected value of buying one ticket for you?what is expected value of you of you buying one ticket for the state?
total number of choices for 6 from 42
= C(42,6) = 5245786
so the prob of winning = 1/5245786
expected winnning = (1/5245786)(10000000) = 1.9
(This lottery is going bankrupt !)
what is the expected value for buying a ticket?
CAN YOU HELP ME
To find the total number of possible results of the drawing in the lottery, we can use the concept of combinations. Since the order in which the numbers are drawn doesn't matter, we can use the formula for combinations.
The formula for combinations is given by nCr = n! / (r!(n-r)!), where n is the total number of possibilities and r is the number of choices.
In this case, there are 42 possibilities and we need to choose 6 numbers, so the calculation would be:
42C6 = 42! / (6! * (42-6)!)
= 42! / (6! * 36!)
= (42 * 41 * 40 * 39 * 38 * 37) / (6 * 5 * 4 * 3 * 2 * 1)
= 5,245,786
Therefore, there are a total of 5,245,786 possible results of the drawing.
To calculate the probability of picking the winning number, we need to determine the total number of possible outcomes and the number of favorable outcomes (i.e., the number of ways to pick the winning number).
The total number of possible outcomes, as we calculated earlier, is 5,245,786.
Now, let's consider the number of favorable outcomes. Since there is only one winning number, the number of favorable outcomes is 1.
So, the probability of picking the winning number would be:
Probability = Favorable outcomes / Total outcomes
= 1 / 5,245,786
≈ 0.00000019
Therefore, the probability of picking the winning number is approximately 0.00000019.
To calculate the expected value of buying one ticket for you, we need to consider the potential outcomes and their respective probabilities and payouts.
In this scenario, there are two possible outcomes: either you win the $10,000,000 or you don't win anything.
The probability of winning the $10,000,000 is the same as the probability of picking the winning number, which we calculated earlier to be approximately 0.00000019.
The probability of not winning anything is the complement of winning, which is 1 minus the probability of winning. So, it would be 1 - 0.00000019 = 0.99999981.
The respective payouts for these outcomes are $10,000,000 and $0.
Now, we can calculate the expected value using the formula:
Expected Value = (Probability of Outcome 1 * Payout of Outcome 1) + (Probability of Outcome 2 * Payout of Outcome 2)
Expected Value = (0.00000019 * $10,000,000) + (0.99999981 * $0)
≈ $1.9
Therefore, the expected value of buying one ticket for you is approximately $1.9.
Similarly, to calculate the expected value of you buying one ticket for the state, we need to consider the potential outcomes, probabilities, and payouts from the state's perspective.
For the state, the potential outcomes are the same: either you win the $10,000,000 or you don't win anything. However, the payouts change.
If you win the $10,000,000, the state needs to pay you $10,000,000. If you don't win, the state keeps the $1 you paid for the ticket.
The probability of winning and not winning remain the same: 0.00000019 and 0.99999981, respectively.
Using the same formula:
Expected Value = (Probability of Outcome 1 * Payout of Outcome 1) + (Probability of Outcome 2 * Payout of Outcome 2)
Expected Value = (0.00000019 * -$10,000,000) + (0.99999981 * $1)
≈ -$1.9
Therefore, the expected value of you buying one ticket for the state is approximately -$1.9.