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You roll a $6$ -sided die two times. $\newline$ What is the probability of rolling a $5$ and then rolling a number less than $4$ ? $\newline$ 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

5

and then rolling a number less than

4

?

\newline

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

\newline

_____

Calculate Probability of Rolling a $5$ : Determine the probability of rolling a $5$ on the first roll. Since there are $6$ possible outcomes on a $6$ -sided die, and only one of those outcomes is a $5$ , the probability of rolling a $5$ is $1$ out of $6$ . Calculation: $P(\text{rolling a } 5) = \frac{1}{6}$
Calculate Probability of Rolling a Number Less Than $4$ : Determine the probability of rolling a number less than $4$ on the second roll. $\newline$ The numbers less than $4$ on a $6$ -sided die are $1$ , $2$ , and $3$ . There are $3$ favorable outcomes out of $6$ possible outcomes. $\newline$ Calculation: $P(\text{rolling a number less than 4}) = \frac{3}{6} = \frac{1}{2}$
Calculate Combined Probability: Since the two rolls are independent events, the probability of both events occurring is the product of their individual probabilities. $\newline$ Calculation: $P(\text{rolling a } 5 \text{ and then rolling a number less than } 4) = P(\text{rolling a } 5) \times P(\text{rolling a number less than } 4) = \frac{1}{6} \times \frac{1}{2}$
Perform Multiplication: Perform the multiplication to find the combined probability. $\newline$ Calculation: $(\frac{1}{6}) \times (\frac{1}{2}) = \frac{1}{12}$

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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of the candidates are randomly chosen to give the first

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Write your answer as a decimal rounded to four decimal places.

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Question

In an experiment, the probability that event

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\frac{2}{7}

, the probability that event

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, and the probability that events

A

B

\frac{1}{9}

\newline

A

B

independent events?

\newline

\newline

\text{yes}

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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

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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

\newline

What is the probability that a randomly chosen competitor reacted in over

0.7

seconds or was female?

\newline

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

\newline

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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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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

1,000

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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\newline

\text{[A]Raffle A}

\newline

\text{[B]Raffle B}

Posted 2 months ago

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

24

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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Question

X

is a normally distributed random variable with mean

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and standard deviation

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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

43

and standard deviation

3

30\%

of the values are those less than ______.

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