Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

A bag contains 2 red marbles, 5 blue marbles and 6 green marbles. If two marbles are drawn out of the bag, what is the exact probability that both marbles drawn will be green? Answer:

A bag contains 22 red marbles, 55 blue marbles and 66 green marbles. If two marbles are drawn out of the bag, what is the exact probability that both marbles drawn will be green?\newlineAnswer:

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Grade 8right chevron icon
Probability of independent and dependent eventsright chevron icon

Full solution

Q. A bag contains 22 red marbles, 55 blue marbles and 66 green marbles. If two marbles are drawn out of the bag, what is the exact probability that both marbles drawn will be green?\newlineAnswer:
  1. Calculate Total Marbles: Determine the total number of marbles in the bag. The bag contains 22 red marbles, 55 blue marbles, and 66 green marbles. To find the total, we add these numbers together. 22 (red) + 55 (blue) + 66 (green) = 1313 (total marbles)
  2. Probability of First Green: Calculate the probability of drawing the first green marble.\newlineThe probability of an event is the number of favorable outcomes divided by the total number of outcomes. For the first draw, the number of favorable outcomes is the number of green marbles, and the total number of outcomes is the total number of marbles in the bag.\newlineProbability of first green marble = Number of green marbles / Total number of marbles = 613\frac{6}{13}
  3. New Total Marbles: Determine the new total number of marbles in the bag after one green marble has been drawn.\newlineAfter drawing one green marble, there is one less green marble and one less marble overall in the bag.\newlineNew total number of marbles = 13−1=1213 - 1 = 12
  4. Probability of Second Green: Calculate the probability of drawing the second green marble after the first has been drawn.\newlineNow, the number of favorable outcomes is the remaining number of green marbles, and the total number of outcomes is the new total number of marbles in the bag.\newlineProbability of second green marble = Remaining number of green marbles / New total number of marbles = 512\frac{5}{12}
  5. Probability of Both Events: Calculate the probability of both events happening together (drawing two green marbles in a row).\newlineTo find the probability of both events happening, we multiply the probability of the first event by the probability of the second event.\newlineProbability of both green marbles = Probability of first green marble ×\times Probability of second green marble = (613)×(512)(\frac{6}{13}) \times (\frac{5}{12})
  6. Perform Multiplication: Perform the multiplication to find the exact probability. (613)×(512)=30156(\frac{6}{13}) \times (\frac{5}{12}) = \frac{30}{156}
  7. Simplify Fraction: Simplify the fraction to its lowest terms.\newline30156\frac{30}{156} can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 66.\newline30÷6=530 \div 6 = 5\newline156÷6=26156 \div 6 = 26\newlineSo, the simplified fraction is 526\frac{5}{26}.

More problems from Probability of independent and dependent events

Question
You roll a 66-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. \newline____ `%`
Get tutor helpright-arrow

Posted 5 months ago

Question
There are 99 college students running for student government class president. The candidates include 77 education majors.\newlineIf 66 of the candidates are randomly chosen to give the first 66 speeches, what is the probability that all of them are education majors?\newlineWrite your answer as a decimal rounded to four decimal places.
Get tutor helpright-arrow

Posted 8 months ago

Question
In an experiment, the probability that event A A occurs is 27 \frac{2}{7} , the probability that event B B occurs is 79 \frac{7}{9} , and the probability that events A A and B B both occur is 19 \frac{1}{9} .\newlineAre A A and B B independent events?\newlineChoices:\newline(A) yes\text{yes}\newline(B) no\text{no}
Get tutor helpright-arrow

Posted 8 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.\newlineThe probability that a competitor reacted in over 0.70.7 seconds is 0.60.6, the probability that a competitor was female is 0.40.4, and the probability that a competitor reacted in over 0.70.7 seconds and was female is 0.30.3.\newlineWhat is the probability that a randomly chosen competitor reacted in over 0.70.7 seconds or was female?\newlineWrite your answer as a whole number, decimal, or simplified fraction.\newline______
Get tutor helpright-arrow

Posted 8 months ago

Question
A restaurant server claims that \(28\)% of the time he leaves candy with the bill, the customer tips well. \newlineIf 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?\newlineWrite your answer as a decimal rounded to the nearest thousandth.
Get tutor helpright-arrow

Posted 7 months 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?\(\$\)_____
Get tutor helpright-arrow

Posted 8 months ago

Question
There are two different raffles you can enter.\newlineIn raffle A, one ticket will win a `$720` prize, and the other tickets will win nothing. There are 1,0001,000 in the raffle, each costing `$11`.\newlineRaffle B is for a `$370` prize. Out of 125125 tickets, each costing `$5`, one ticket will win the prize, and the other tickets will win nothing.\newlineWhich raffle is a better deal?\newlineChoices:\newline[A]Raffle A\text{[A]Raffle A}\newline[B]Raffle B\text{[B]Raffle B}
Get tutor helpright-arrow

Posted 8 months ago

Question
XX is a normally distributed random variable with mean 4949 and standard deviation 2525.\newlineWhat is the probability that XX is between 2424 and 7474??\newlineUse the 0.68−0.95−0.9970.68-0.95-0.997 rule and write your answer as a decimal. Round to the nearest thousandth if necessary.\newline____
Get tutor helpright-arrow

Posted 8 months ago

Question
XX is a normally distributed random variable with mean 6565 and standard deviation 88.\newlineWhat is the probability that XX is between 6262 and 6868??\newlineWrite your answer as a decimal rounded to the nearest thousandth.\newline____
Get tutor helpright-arrow

Posted 8 months ago

Question
Complete the statement. Round your answer to the nearest thousandth.\newlineIn a population that is normally distributed with mean 4343 and standard deviation 33, the bottom 30%30\% of the values are those less than ______.
Get tutor helpright-arrow

Posted 8 months ago

View all (56)

Related topics

Algebra - Order of OperationsAlgebra - Distributive Property`X` and `Y` AxesGeometry - Scalene TriangleCommon MultipleGeometry - Quadrant