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You roll a $6$ -sided die two times. $\newline$ What is the probability of rolling an odd number and then rolling an even number? $\newline$ 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 an odd number and then rolling an even number?

\newline

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

\newline

_____

Identify Odd and Even Numbers: There are $3$ odd numbers ( $1$ , $3$ , $5$ ) and $3$ even numbers ( $2$ , $4$ , $6$ ) on a $6$ -sided die. The probability of rolling an odd number on the first roll is the number of odd outcomes divided by the total number of outcomes.
Calculate Probability of Rolling Odd Number: The probability of rolling an odd number on the first roll is $\frac{3}{6}$ , which simplifies to $\frac{1}{2}$ .
Calculate Probability of Rolling Even Number: The probability of rolling an even number on the second roll is also $\frac{3}{6}$ , which simplifies to $\frac{1}{2}$ , because the outcome of the second roll is independent of the first roll.
Multiply Probabilities for Combined Probability: To find the combined probability of two independent events, we multiply the probabilities of each event occurring. So, we multiply the probability of rolling an odd number by the probability of rolling an even number.
Multiply Probabilities for Combined Probability: To find the combined probability of two independent events, we multiply the probabilities of each event occurring. So, we multiply the probability of rolling an odd number by the probability of rolling an even number.The combined probability is $(\frac{1}{2}) \times (\frac{1}{2}) = \frac{1}{4}$ .

More problems from Probability of independent and dependent events

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6

-sided die two times. What is the probability of rolling a number greater than \(3\) and then rolling a number less than \(4\)? Write your answer as a percentage. ____ `%`

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9

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

7

education majors.

\newline

6

of the candidates are randomly chosen to give the first

6

speeches, what is the probability that all of them are education majors?

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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

A

\frac{2}{7}

, the probability that event

B

\frac{7}{9}

, and the probability that events

A

B

\frac{1}{9}

\newline

A

B

independent events?

\newline

\newline

\text{yes}

\newline

\text{no}

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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

0.4

, and the probability that a competitor reacted in over

0.7

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

Posted 3 months ago

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?

\newline

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

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?

\newline

\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

25

\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

Posted 3 months ago

Question

X

is a normally distributed random variable with mean

65

and standard deviation

8

\newline

What is the probability that

X

62

68

?

\newline

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

\newline

Posted 3 months ago

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 ______.

Posted 3 months ago