1.
what is the sample space of the product of two 6-sided die where the first number is 6?
list your values from smallest to largest.
The sample space of rolling two 6-sided dice consists of all possible outcomes when rolling the dice. If we are looking for the product of the two dice where the first number is 6, the possible outcomes would be:
6*1 = 6
6*2 = 12
6*3 = 18
6*4 = 24
6*5 = 30
6*6 = 36
So the sample space of the product of two 6-sided dice where the first number is 6 is: {6, 12, 18, 24, 30, 36}
2.
John has to make all free throws to win the game. assume each free throw is an independent event and that the pressure of the situation has no impact on him. if john is a 55% free throw shooter what is the percent chance that john makes all three throws? do not round your answer.
If John has a 55% chance of making a free throw, this means he has a 0.55 probability of making each throw and a 0.45 probability of missing each throw.
For John to make all three throws, the probability is calculated by multiplying the individual probabilities:
0.55 * 0.55 * 0.55 = 0.166375
Therefore, the percent chance that John makes all three throws is 16.6375%.
3.
what is the probability of flipping a fair coin and it landing on heads and rolling a 3 on a fair six sided die?
When flipping a fair coin and rolling a fair six-sided die, the outcomes are independent of each other.
For the coin flip, there are two equally likely outcomes: heads and tails. The probability of the coin landing on heads is 1/2.
For the six-sided die, there are six equally likely outcomes: 1, 2, 3, 4, 5, and 6. The probability of rolling a 3 is 1/6.
Since the outcomes are independent, the overall probability of both events occurring is calculated by multiplying the probabilities of each event:
(1/2) * (1/6) = 1/12
Therefore, the probability of flipping a fair coin and it landing on heads and rolling a 3 on a fair six-sided die is 1/12.
4.
a math quiz has 5 multiple choice questions and each question has 3 choices. if a student has to guess (and is not able to remove any of the incorrect choices) what is the probability that the student answers all of the questions correctly?
Since each question has 3 choices and the student has to guess without the ability to remove any incorrect choices, the probability of guessing the correct answer for each question is 1/3.
There are 5 questions in total, so the probability that the student answers all of the questions correctly by guessing on each one is:
(1/3)^5 = 1/243
Therefore, the probability that the student answers all of the questions correctly by guessing is 1/243.
5.
your employer is offering free tickets for two baseball games. they play 53 home games and 8 of them are against the Snakes. the tickets are randomly given out. what is the probability that both are games are against the Snakes? write your answer as a fraction. you do not need to simplify.
There are a total of 53 home games, and 8 of them are against the Snakes.
The probability of being given a ticket for an "against the Snakes" game for the first ticket is 8 out of 53.
Since the tickets are randomly given out, the probability of getting a second ticket for an "against the Snakes" game is also 8 out of 53.
To find the probability of both tickets being for "against the Snakes" games, we multiply the probabilities:
(8/53) * (8/53) = 64/2809
Therefore, the probability that both tickets are for games against the Snakes is 64/2809.