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:

You choose a card at random. Without putting the first card back, you choose a second card at random. What is the probability of choosing a 1010 and then choosing a Jack? Write your answer as a fraction or whole number.

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 1right chevron icon
Probability of independent and dependent eventsright chevron icon

Full solution

Q. You choose a card at random. Without putting the first card back, you choose a second card at random. What is the probability of choosing a 1010 and then choosing a Jack? Write your answer as a fraction or whole number.
  1. Determine total ways: First, we need to determine the total number of ways to choose any card from a deck. A standard deck of cards has 5252 cards. So, the total number of ways to choose the first card is 5252.
  2. Calculate 1010 probability: Next, we calculate the probability of choosing a 1010 as the first card. There are four 1010s in a deck (one for each suit), so the probability of choosing a 1010 on the first draw is the number of 1010s divided by the total number of cards.\newlineP(Choosing a 10)=Number of 10sTotal number of cards=452P(\text{Choosing a 10}) = \frac{\text{Number of 10s}}{\text{Total number of cards}} = \frac{4}{52}
  3. Calculate Jack probability: After choosing a 1010, we do not put it back in the deck, so now there are 5151 cards left. We need to calculate the probability of choosing a Jack from the remaining cards.
  4. Find overall probability: There are four Jacks in a deck. So, the probability of choosing a Jack after a 1010 has been chosen is the number of Jacks divided by the remaining number of cards.P(Choosing a Jack after a 10)=Number of JacksRemaining number of cards=451P(\text{Choosing a Jack after a } 10) = \frac{\text{Number of Jacks}}{\text{Remaining number of cards}} = \frac{4}{51}
  5. Perform multiplication: To find the overall probability of both events happening in sequence (choosing a 1010 and then a Jack), we multiply the probabilities of each individual event.\newlineP(Choosing a 10 and then a Jack)=P(Choosing a 10)×P(Choosing a Jack after a 10)=(452)×(451)P(\text{Choosing a } 10 \text{ and then a Jack}) = P(\text{Choosing a } 10) \times P(\text{Choosing a Jack after a } 10) = \left(\frac{4}{52}\right) \times \left(\frac{4}{51}\right)
  6. Find probability: Now we perform the multiplication to find the probability. P(Choosing a 10 and then a Jack)=452×451=162652P(\text{Choosing a 10 and then a Jack}) = \frac{4}{52} \times \frac{4}{51} = \frac{16}{2652}
  7. Simplify fraction: We can simplify the fraction by dividing both the numerator and the denominator by the greatest common divisor, which is 44.P(Choosing a 10 and then a Jack)=164/26524=4663P(\text{Choosing a } 10 \text{ and then a Jack}) = \frac{16}{4} / \frac{2652}{4} = \frac{4}{663}
  8. Final probability: The simplified probability of choosing a 1010 and then a Jack without replacement is 4663\frac{4}{663}.

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 (18)

Related topics

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