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:

Malia is shopping for a costume at a thrift store. There are 88 costumes hanging on the rack, including 66 witch costumes.\newlineIf the costumes all look like the right size, and Malia randomly selects 44 to try on, what is the probability that all of them are witch costumes?\newlineWrite your answer as a decimal rounded to four decimal places.\newline____\newline

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Precalculusright chevron icon
Find probabilities using combinations and permutationsright chevron icon

Full solution

Q. Malia is shopping for a costume at a thrift store. There are 88 costumes hanging on the rack, including 66 witch costumes.\newlineIf the costumes all look like the right size, and Malia randomly selects 44 to try on, what is the probability that all of them are witch costumes?\newlineWrite your answer as a decimal rounded to four decimal places.\newline____\newline
  1. Calculate Probability of First Pick: First, calculate the probability of picking a witch costume on the first try.\newlineThere are 66 witch costumes out of 88, so the probability is 68\frac{6}{8}.
  2. Calculate Probability of Second Pick: Next, calculate the probability of picking a witch costume on the second try, given that the first one was a witch costume.\newlineNow there are 55 witch costumes left and 77 costumes in total, so the probability is 57\frac{5}{7}.
  3. Calculate Probability of Third Pick: Then, calculate the probability of picking a witch costume on the third try, given that the first two were witch costumes.\newlineNow there are 44 witch costumes left and 66 costumes in total, so the probability is 46.\frac{4}{6}.
  4. Calculate Probability of Fourth Pick: Finally, calculate the probability of picking a witch costume on the fourth try, given that the first three were witch costumes.\newlineNow there are 33 witch costumes left and 55 costumes in total, so the probability is 35\frac{3}{5}.
  5. Multiply Probabilities: Now, multiply all the probabilities together to get the overall probability of picking 44 witch costumes in a row. 68×57×46×35=6×5×4×38×7×6×5\frac{6}{8} \times \frac{5}{7} \times \frac{4}{6} \times \frac{3}{5} = \frac{6\times5\times4\times3}{8\times7\times6\times5}
  6. Simplify Multiplication: Simplify the multiplication and cancel out common factors.\newlineThe 6s6s and the 5s5s cancel out, leaving (4×3)/(8×7)(4 \times 3)/(8 \times 7).
  7. Perform Multiplication: Now, perform the multiplication. 4×3=124\times3 = 12 and 8×7=568\times7 = 56, so the probability is 1256.\frac{12}{56}.
  8. Simplify Fraction: Simplify the fraction 1256\frac{12}{56} by dividing both the numerator and the denominator by their greatest common divisor, which is 44. 12÷4=312 \div 4 = 3 and 56÷4=1456 \div 4 = 14, so the simplified probability is 314\frac{3}{14}.
  9. Convert to Decimal: Finally, convert the fraction to a decimal and round to four decimal places. 314≈0.2143\frac{3}{14} \approx 0.2143

More problems from Find probabilities using combinations and permutations

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 9 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 9 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 9 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 9 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 9 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 9 months ago

View all (20)

Related topics

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