Studdy AI Logo
Math

QuestionA bag has 6 red, 10 green, 9 blue, and 11 yellow M&Ms. Find the probabilities of picking: 1) yellow, 2) blue or green, 3) orange.

Studdy Solution

STEP 1

Assumptions1. The bag contains6 red,10 green,9 blue, and11 yellow M&M's. . Each M&M is equally likely to be picked.
3. The M&M's are picked without replacement.

STEP 2

First, we need to find the total number of M&M's in the bag. We can do this by adding the number of each color of M&M's.
Total M&M′s=Red+Green+Blue+YellowTotal\, M\&M's = Red + Green + Blue + Yellow

STEP 3

Now, plug in the given values for the number of each color of M&M's to calculate the total number of M&M's.
Total M&M′s=6+10+9+11Total\, M\&M's =6 +10 +9 +11

STEP 4

Calculate the total number of M&M's.
Total M&M′s=6+10+9+11=36Total\, M\&M's =6 +10 +9 +11 =36

STEP 5

The probability of an event is the ratio of the number of ways the event can occur to the total number of outcomes. So, the probability of picking a yellow M&M is the ratio of the number of yellow M&M's to the total number of M&M's.
(Yellow)=Number of yellow M&M′sTotal M&M′s(Yellow) = \frac{Number\, of\, yellow\, M\&M's}{Total\, M\&M's}

STEP 6

Plug in the values for the number of yellow M&M's and the total number of M&M's to calculate the probability of picking a yellow M&M.
(Yellow)=1136(Yellow) = \frac{11}{36}

STEP 7

The probability of picking a blue or green M&M is the sum of the probabilities of picking a blue M&M and picking a green M&M.
(Blue or Green)=(Blue)+(Green)(Blue\, or\, Green) =(Blue) +(Green)

STEP 8

Calculate the probabilities of picking a blue M&M and a green M&M.
(Blue)=Number of blue M&M′sTotal M&M′s=36(Blue) = \frac{Number\, of\, blue\, M\&M's}{Total\, M\&M's} = \frac{}{36}(Green)=Number of green M&M′sTotal M&M′s=1036(Green) = \frac{Number\, of\, green\, M\&M's}{Total\, M\&M's} = \frac{10}{36}

STEP 9

Now, plug in the values for(Blue) and(Green) to calculate(Blue or Green).
(Blue or Green)=936+36(Blue\, or\, Green) = \frac{9}{36} + \frac{}{36}

STEP 10

Calculate the probability of picking a blue or green M&M.
(Blue or Green)=936+1036=1936(Blue\, or\, Green) = \frac{9}{36} + \frac{10}{36} = \frac{19}{36}

STEP 11

The probability of picking an orange M&M is0, since there are no orange M&M's in the bag.
(Orange)=0(Orange) =0So, the probability of picking a yellow M&M is 1136\frac{11}{36}, the probability of picking a blue or green M&M is 1936\frac{19}{36}, and the probability of picking an orange M&M is0.

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