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You roll a $6$ -sided die two times. $\newline$ What is the probability of rolling a $1$ and then rolling a number less than $2$ ? $\newline$ Simplify your answer and write it as a fraction or whole number. $\newline$ _____

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Probability of independent and dependent events

Full solution

Q. You roll a

6

-sided die two times.

\newline

What is the probability of rolling a

1

and then rolling a number less than

2

?

\newline

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

\newline

_____

Determine Probability of Rolling a $1$ : First, we need to determine the probability of rolling a $1$ on a $6$ -sided die. Since there are $6$ possible outcomes and only one of them is a $1$ , the probability of rolling a $1$ is $1$ out of $6$ . $\newline$ Calculation: $P(\text{rolling a } 1) = \frac{1}{6}$
Find Probability of Rolling a Number Less Than $2$ : Next, we need to determine the probability of rolling a number less than $2$ on the second roll. The only number less than $2$ on a $6$ -sided die is $1$ . Therefore, the probability of rolling a number less than $2$ is the same as the probability of rolling a $1$ , which is $1$ out of $6$ . $\newline$ Calculation: $P(\text{rolling a number less than } 2) = \frac{1}{6}$
Calculate Combined Probability: Now, we need to find the combined probability of both events happening in sequence. Since the two rolls are independent events, we multiply the probabilities of each event occurring. $\newline$ Calculation: $P(\text{rolling a } 1 \text{ and then rolling a number less than } 2) = P(\text{rolling a } 1) \times P(\text{rolling a number less than } 2) = \left(\frac{1}{6}\right) \times \left(\frac{1}{6}\right)$
Perform Final Multiplication: Performing the multiplication gives us the final probability. $\newline$ Calculation: $(\frac{1}{6}) \times (\frac{1}{6}) = \frac{1}{36}$

More problems from Probability of independent and dependent events

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

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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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B

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\newline

\text{yes}

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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

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Question

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

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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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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.

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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`.

\newline

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

125

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}

\newline

\text{[B]Raffle B}

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Question

X

is a normally distributed random variable with mean

49

and standard deviation

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\newline

What is the probability that

X

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74

?

\newline

0.68-0.95-0.997

rule and write your answer as a decimal. Round to the nearest thousandth if necessary.

\newline

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X

is a normally distributed random variable with mean

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\newline

What is the probability that

X

62

68

?

\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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3

30\%

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