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You pick a card at random. Without putting the first card back, you pick a second card at random. $\newline$ $123$ $\newline$ What is the probability of picking a $3$ and then picking a $2$ ? $\newline$ Write your answer as a fraction or whole number. $\newline$ $\_\_\_$

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Probability of independent and dependent events

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Q. You pick a card at random. Without putting the first card back, you pick a second card at random.

\newline

123

\newline

What is the probability of picking a

3

and then picking a

2

?

\newline

Write your answer as a fraction or whole number.

\newline

\_\_\_

Identify Cards: Identify the total number of cards in a standard deck and the specific cards of interest. $\newline$ A standard deck has $52$ cards. There are four $3$ s and four $2$ s in the deck.
Calculate Probability of $3$ : Calculate the probability of drawing a $3$ first. $\newline$ The probability of picking a $3$ from the deck is $4$ out of $52$ , which simplifies to $\frac{1}{13}$ .
Calculate Probability of $2$ : Calculate the probability of drawing a $2$ after a $3$ has been drawn. $\newline$ After drawing a $3$ , there are $51$ cards left and still four $2$ s. The probability of now drawing a $2$ is $4$ out of $51$ .
Multiply Probabilities: Multiply the probabilities of the two independent events. The overall probability of both events occurring in sequence is $(\frac{1}{13}) \times (\frac{4}{51}) = \frac{4}{663}$ .

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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\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 9 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 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

Posted 9 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 9 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 9 months ago

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