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What is the probability of flipping heads and rolling a six? $\newline$ $\newline$ Write your answer as a fractions" target="_blank" class="backlink">fraction or a whole number. With fractions, use a slash ( $/$ ) to separate the numerator and denominator. $\newline$ $\_\_$

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Probability of compound events

Full solution

Q. What is the probability of flipping heads and rolling a six?

\newline

\newline

Write your answer as a fraction or a whole number. With fractions, use a slash (

/

) to separate the numerator and denominator.

\newline

\_\_

Calculate Probability of Flipping Heads: Step $1$ : Determine the probability of flipping heads. $\newline$ The probability of flipping heads on a fair coin is $1$ out of $2$ possible outcomes (heads or tails). $\newline$ Calculation: Probability of heads = $\frac{1}{2}$
Calculate Probability of Rolling a Six: Step $2$ : Determine the probability of rolling a six on a fair six-sided die. $\newline$ The probability of rolling a six is $1$ out of $6$ possible outcomes ( $1$ , $2$ , $3$ , $4$ , $5$ , or $6$ ). $\newline$ Calculation: Probability of rolling a six = $\frac{1}{6}$
Calculate Combined Probability: Step $3$ : Calculate the combined probability of both independent events happening (flipping heads and rolling a six). $\newline$ To find the combined probability of two independent events, multiply the probabilities of each event. $\newline$ Calculation: Combined probability = $(\frac{1}{2}) \times (\frac{1}{6}) = \frac{1}{12}$

More problems from Probability of compound events

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6

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\newline

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

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education majors.

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6

of the candidates are randomly chosen to give the first

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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

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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?

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\newline

\text{yes}

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\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.

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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

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\newline

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

\newline

Posted 9 months ago

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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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.

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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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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?

\newline

\newline

\text{[A]Raffle A}

\newline

\text{[B]Raffle B}

Posted 8 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

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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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What is the probability that

X

62

68

?

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

\newline

Posted 9 months ago

Question

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

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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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