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You roll a $6$ -sided die. $\newline$ What is $P(6)$ ? $\newline$ $\newline$ Simplify your answer and write it as a fraction or whole number. $\newline$ _____

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Theoretical probability

Full solution

Q. You roll a

6

-sided die.

\newline

What is

P(6)

?

\newline

\newline

Simplify your answer and write it as a fraction or whole number.

\newline

_____

Identify total possible outcomes: Identify the total number of possible outcomes when rolling a $6$ -sided die. $\newline$ A $6$ -sided die has $6$ faces, each with a different number from $1$ to $6$ . Therefore, there are $6$ possible outcomes when the die is rolled.
Determine favorable outcomes: Determine the number of favorable outcomes for rolling a $6$ . Since there is only one face with the number $6$ , there is only one favorable outcome for this event.
Calculate probability: Calculate the probability of rolling a $6$ . The probability of an event is given by the ratio of the number of favorable outcomes to the total number of possible outcomes. In this case, the probability $P(6)$ is: $P(6) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}$ $P(6) = \frac{1}{6}$

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college students running for student government class president. The candidates include

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of the candidates are randomly chosen to give the first

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Question

In an experiment, the probability that event

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, the probability that event

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, and the probability that events

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B

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\newline

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Question

At a science museum, visitors can compete to see who has a faster reaction time. Competitors watch a red screen, and the moment they see it turn from red to green, they push a button. The machine records their reaction times and also asks competitors to report their gender.

\newline

The probability that a competitor reacted in over

0.7

0.6

, the probability that a competitor was female is

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, and the probability that a competitor reacted in over

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seconds and was female is

0.3

\newline

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Write your answer as a whole number, decimal, or simplified fraction.

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Question

A restaurant server claims that \(28\)% of the time he leaves candy with the bill, the customer tips well.

\newline

If the server's claim is true, and one day he leaves candy with \(4\) customers' bills, what is the probability that exactly \(3\) of those customers will tip well?

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Write your answer as a decimal rounded to the nearest thousandth.

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Question

There is a spinner with `50` equally likely sections, numbered from `1` to `50`. You have the opportunity to spin it. If the number is odd, you win $`11`. If the number is even, you win nothing. If you play the game, what is the expected payoff?\(\$\)_____

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Question

There are two different raffles you can enter.

\newline

In raffle A, one ticket will win a `$720` prize, and the other tickets will win nothing. There are

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in the raffle, each costing `$11`.

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Raffle B is for a `$370` prize. Out of

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tickets, each costing `$5`, one ticket will win the prize, and the other tickets will win nothing.

\newline

Which raffle is a better deal?

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\text{[A]Raffle A}

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\text{[B]Raffle B}

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Question

X

is a normally distributed random variable with mean

49

and standard deviation

25

\newline

What is the probability that

X

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74

?

\newline

0.68-0.95-0.997

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\newline

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Question

X

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\newline

What is the probability that

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?

\newline

Write your answer as a decimal rounded to the nearest thousandth.

\newline

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Question

Complete the statement. Round your answer to the nearest thousandth.

\newline

In a population that is normally distributed with mean

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and standard deviation

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30\%

of the values are those less than ______.

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