Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

A bag contains $6$ red balls, $4$ green balls, and $3$ blue balls. If we choose a ball, then another ball without putting the first one back in the bag, what is the probability that the first ball will be green and the second will be red?

View step-by-step help

View step-by-step help

Probability of independent and dependent events

Full solution

Q. A bag contains

6

red balls,

4

green balls, and

3

blue balls. If we choose a ball, then another ball without putting the first one back in the bag, what is the probability that the first ball will be green and the second will be red?

Calculate Total Number of Balls: Calculate the total number of balls in the bag. $\newline$ The bag contains $6$ red balls, $4$ green balls, and $3$ blue balls. So, the total number of balls is $6 + 4 + 3 = 13$ balls.
Calculate Probability of Drawing Green Ball: Calculate the probability of drawing a green ball first. $\newline$ Since there are $4$ green balls and the total number of balls is $13$ , the probability of drawing a green ball first is $\frac{4}{13}$ .
Calculate Number of Balls Left: Calculate the number of balls left after drawing one green ball. $\newline$ After one green ball is drawn, there are $13 - 1 = 12$ balls left in the bag.
Calculate Probability of Drawing Red Ball: Calculate the probability of drawing a red ball after drawing a green ball. Since there are still $6$ red balls left and now only $12$ balls in total, the probability of drawing a red ball after a green ball is $\frac{6}{12}$ .
Calculate Combined Probability: Calculate the combined probability of both events happening in sequence. $\newline$ To find the combined probability of drawing a green ball first and then a red ball, we multiply the probabilities of each individual event. So, the combined probability is $(\frac{4}{13}) \times (\frac{6}{12})$ .
Simplify Combined Probability: Simplify the combined probability. $\newline$ The combined probability simplifies to $(\frac{4}{13}) \times (\frac{1}{2}) = \frac{4}{26} = \frac{2}{13}$ after simplifying the fraction.

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 3 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 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.

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 3 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 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