1)Suppose you buy 1 ticket for $1 out of a lottery of 3000 tickets. If the prize for the one winning

ticket is to be $500, what are your expected winnings? I'm assuming the answer for this one is $0.00

2)A basketball player with a free throw shooting percentage of 60% gets fouled and goes to the line
to shoot two free throws. What are the odds in favor of her making her first shot? Is the answer 3:5

3)Two dice are rolled. Find the odds that the score on the dice is either 10 or at most 5. Now for this one I came up with 1:2

Can someone please check if I came up with the correct answers. I'm studying for my quiz

On the first: THe expected value is 500/3000 or .17 dollars.

second: correct

third: ten can be had by 5,5, or 6,4, or 4,6 Probability is 1/36 + 2/36= 3/35
at most five means 1,1, 1,2, 1,3, 1,4, 2,3 probab is 1/36+ 2/36+2/36 + 2/36 + 2/36 or 9/36

so total prob is 12/36 or 1/3 or odd 1:2 as you deduced.

bobpursley on the first one it's a mult. choice which I have

A) $0.00 B) -$1.00 C) -$0.85 D) -$0.83 where did you get $17 though? I don't understand this one.

1) To find the expected winnings, we need to multiply the probability of winning by the amount won and subtract the cost of buying the ticket.

In this case, the probability of winning is 1/3000 (since there is only one winning ticket out of 3000). The amount won is $500. The cost of buying the ticket is $1.

Expected winnings = (Probability of winning * Amount won) - Cost of buying the ticket
Expected winnings = (1/3000 * $500) - $1
Expected winnings = ($500/3000) - $1
Expected winnings = $0.1667 - $1
Expected winnings = -$0.8333

So, your expected winnings from buying one ticket are -$0.8333, which means you can expect to lose money on average.

2) To find the odds in favor of making the first shot, we need to divide the probability of making the first shot by the probability of missing the first shot.

The probability of making the first shot is 60% or 0.6.
The probability of missing the first shot is 1 - 0.6 = 0.4.

Odds in favor = Probability of making the first shot / Probability of missing the first shot
Odds in favor = 0.6 / 0.4
Odds in favor = 3/2 or 3:2

So, the odds in favor of making the first shot are 3:2.

3) To find the odds that the score on the dice is either 10 or at most 5, we need to calculate the number of favorable outcomes and divide it by the number of possible outcomes.

The favorable outcomes are:
- Getting a score of 10: That can happen with (4, 6), (5, 5), or (6, 4) on the two dice. So, there are 3 favorable outcomes for scoring 10.
- Getting a score at most 5: That can happen with (1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (2, 1), (2, 2), (2, 3), (2, 4), (3, 1), (3, 2), (3, 3), (4, 1), (4, 2), (5, 1), or (5, 2) on the two dice. So, there are 15 favorable outcomes for scoring at most 5.

The possible outcomes are:
- Rolling two dice: Each die has 6 possible outcomes, so the total number of possible outcomes is 6 * 6 = 36.

Odds in favor = Number of favorable outcomes / Number of possible outcomes
Odds in favor = (3 + 15) / 36
Odds in favor = 18 / 36
Odds in favor = 1/2 or 1:2

So, the odds that the score on the dice is either 10 or at most 5 are 1:2.

1) To find your expected winnings, you need to calculate the probability of winning the prize and multiply it by the amount of the prize.

In this case, there is only one winning ticket out of 3000 tickets, so the probability of winning is 1/3000. The prize for the winning ticket is $500.

Expected winnings = (Probability of winning) x (Prize amount)
= (1/3000) x ($500)
= $0.1667

So, your expected winnings are approximately $0.1667, which rounds to $0.00.

Your answer of $0.00 is correct.

2) The odds in favor of making the first shot can be calculated by dividing the probability of making the shot by the probability of missing it.

The player has a free throw shooting percentage of 60%, which means the probability of making a shot is 60%. Therefore, the probability of missing the shot is 40%.

Odds in favor of making the first shot = Probability of making the shot / Probability of missing the shot
= 60% / 40%
= 3/2

So, the odds in favor of making the first shot are 3:2.

Your answer of 3:5 is incorrect.

3) To find the odds of getting a score of either 10 or at most 5 when two dice are rolled, we need to count the number of favorable outcomes and divide it by the total number of possible outcomes.

First, let's find the number of favorable outcomes:
- Getting a score of 10: There are 3 ways to get a score of 10 (4+6, 5+5, 6+4).
- Getting a score at most 5: There are 15 ways to get a score of at most 5 (1+1, 1+2, 1+3, 1+4, 1+5, 2+1, 2+2, 2+3, 2+4, 3+1, 3+2, 3+3, 4+1, 4+2, 5+1).

The total number of possible outcomes when rolling two dice is 6 x 6 = 36.

Odds = Number of favorable outcomes / Total number of possible outcomes
= (3+15) / 36
= 18 / 36
= 1/2

So, the odds of getting a score of either 10 or at most 5 are 1:2.

Your answer of 1:2 is correct.

Good luck with your quiz!