Studdy AI Logo
Math  /  Data & Statistics

QuestionSuppose a box contains 2 blue, 2 red, 3 purple, and 3 green pencils.
Find P(P( not red|not green).

Studdy Solution

STEP 1

1. The box contains a total of 10 pencils: 2 blue, 2 red, 3 purple, and 3 green.
2. We are looking for the probability of selecting a pencil that is not red given that it is not green.

STEP 2

1. Determine the total number of pencils that are not green.
2. Determine the number of pencils that are not red and not green.
3. Calculate the conditional probability.

STEP 3

Count the total number of pencils that are not green. Since there are 3 green pencils, the remaining pencils are:
10−3=7 10 - 3 = 7

STEP 4

Count the number of pencils that are neither red nor green. The pencils that are not red are blue and purple. There are:
- 2 blue pencils - 3 purple pencils
Thus, the total number of pencils that are not red and not green is:
2+3=5 2 + 3 = 5

STEP 5

Calculate the conditional probability P(not red∣not green) P(\text{not red} \mid \text{not green}) using the formula:
P(not red∣not green)=Number of pencils that are not red and not greenTotal number of pencils that are not green P(\text{not red} \mid \text{not green}) = \frac{\text{Number of pencils that are not red and not green}}{\text{Total number of pencils that are not green}}
Substitute the values:
P(not red∣not green)=57 P(\text{not red} \mid \text{not green}) = \frac{5}{7}
The probability is:
57 \boxed{\frac{5}{7}}

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