Math

QuestionCalculate the probability of drawing 2 chocolates from a bag with 12 chocolates, 5 gums, and 4 taffies. Round to three decimals.

Studdy Solution

STEP 1

Assumptions1. The bag contains12 chocolates,5 pieces of gum, and4 pieces of taffy. . We are pulling out pieces from the bag without replacement.
3. We want to find the probability that both pieces are chocolates.

STEP 2

First, we need to find the total number of pieces in the bag. We can do this by adding the number of chocolates, pieces of gum, and pieces of taffy.
Totalpieces=Chocolates+Gum+affyTotal\, pieces = Chocolates + Gum +affy

STEP 3

Now, plug in the given values for the number of chocolates, pieces of gum, and pieces of taffy to calculate the total number of pieces.
Totalpieces=12+5+Total\, pieces =12 +5 +

STEP 4

Calculate the total number of pieces in the bag.
Totalpieces=12++4=21Total\, pieces =12 + +4 =21

STEP 5

The probability of drawing a chocolate on the first draw is the number of chocolates divided by the total number of pieces.
(Chocolateonfirstdraw)=ChocolatesTotalpieces(Chocolate\, on\, first\, draw) = \frac{Chocolates}{Total\, pieces}

STEP 6

Plug in the values for the number of chocolates and the total number of pieces to calculate the probability of drawing a chocolate on the first draw.
(Chocolateonfirstdraw)=1221(Chocolate\, on\, first\, draw) = \frac{12}{21}

STEP 7

After one chocolate is drawn, there are now11 chocolates left and20 total pieces. The probability of drawing a chocolate on the second draw is the number of remaining chocolates divided by the total number of remaining pieces.
(Chocolateonseconddraw)=Chocolates1Totalpieces1(Chocolate\, on\, second\, draw) = \frac{Chocolates -1}{Total\, pieces -1}

STEP 8

Plug in the values for the number of chocolates and the total number of pieces to calculate the probability of drawing a chocolate on the second draw.
(Chocolateonseconddraw)=121211(Chocolate\, on\, second\, draw) = \frac{12 -1}{21 -1}

STEP 9

Calculate the probability of drawing a chocolate on the second draw.
(Chocolateonseconddraw)=1120(Chocolate\, on\, second\, draw) = \frac{11}{20}

STEP 10

The probability of both events occurring is the product of their individual probabilities.
(Bothchocolates)=(Chocolateonfirstdraw)times(Chocolateonseconddraw)(Both\, chocolates) =(Chocolate\, on\, first\, draw) \\times(Chocolate\, on\, second\, draw)

STEP 11

Plug in the values for the probability of drawing a chocolate on the first draw and the probability of drawing a chocolate on the second draw to calculate the probability of both pieces being chocolates.
(Bothchocolates)=21times1120(Both\, chocolates) = \frac{}{21} \\times \frac{11}{20}

STEP 12

Calculate the probability of both pieces being chocolates.
(Bothchocolates)=1221times1120=0.314(Both\, chocolates) = \frac{12}{21} \\times \frac{11}{20} =0.314The probability that both pieces are chocolates is0.314.

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord