Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

You roll a $6$ -sided die two times. $\newline$ What is the probability of rolling an even number and then rolling a number less than $4$ ? $\newline$ Simplify your answer and write it as a fraction or whole number. $\newline$ _____

View step-by-step help

View step-by-step help

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 even number and then rolling a number less than

4

?

\newline

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

\newline

_____

Identify Total Outcomes: Identify the total number of possible outcomes for one roll of a $6$ -sided die. $\newline$ Since a $6$ -sided die has $6$ faces, there are $6$ possible outcomes for each roll.
Favorable Outcomes (Even): Determine the number of favorable outcomes for the first event (rolling an even number). $\newline$ The even numbers on a $6$ -sided die are $2$ , $4$ , and $6$ . There are $3$ even numbers.
Favorable Outcomes (Less than $4$ ): Determine the number of favorable outcomes for the second event (rolling a number less than $4$ ). $\newline$ The numbers less than $4$ on a $6$ -sided die are $1$ , $2$ , and $3$ . There are $3$ numbers less than $4$ .
Calculate Probability: Calculate the probability of both events happening in sequence. $\newline$ Since the two rolls are independent events, the probability of both occurring is the product of their individual probabilities. $\newline$ Probability of rolling an even number on the first roll = Number of even numbers / Total number of outcomes = $\frac{3}{6}$ $\newline$ Probability of rolling a number less than $4$ on the second roll = Number of numbers less than $4$ / Total number of outcomes = $\frac{3}{6}$
Multiply Probabilities: Multiply the probabilities of the two independent events to find the combined probability. Combined probability = $(\frac{3}{6}) \times (\frac{3}{6})$
Simplify Probability: Simplify the combined probability. $\newline$ Combined probability = $(\frac{1}{2}) \times (\frac{1}{2}) = \frac{1}{4}$

More problems from Probability of independent and dependent events

Question

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. ____ `%`

Posted 1 month ago

Question

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?

\newline

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

Posted 2 months ago

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}

Posted 2 months ago

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 2 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.

Posted 1 month ago

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?\(\$\)_____

Posted 2 months ago

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 2 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 2 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 2 months ago