SOLUTION: Alexis often gets her clothes dirty during meals because she's a messy eater especially eating pasta. Her mother cooks pasta twice a week. so if Alexis has pasta. her clothing is d

Question 1001678: Alexis often gets her clothes dirty during meals because she's a messy eater especially eating pasta. Her mother cooks pasta twice a week. so if Alexis has pasta. her clothing is dirty 1 out of 2 times. Days Alexis does not have pasta, her clothes are clean 2 out of 3. what is the probability she would have a clean dress today
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
clean means her clothes are clean.
dirty means her clothes are dirty.
pasta means she ate pasta.
no pasta means she didn't eat pasta.

you are given that her mother cooks pasta for her 2 times a week.

therefore:

p(pasta) = 2/7
p(no pasta) = 5/7

you are given that her clothes are dirty 1 out of 2 times that she eats pasta.

this means that her clothese are clean 1 out of 2 times that she eats pasta.

therefore:

p(clean given pasta) = 1/2

you are given that her clothes are clean 2 out of 3 times that she doesn't eat pasta.

therefore:

p(clean given no pasta) = 2/3

you want to know the probability that she'll have a clean dress today.

the probability that she'll have a clean dress today = p(pasta) * p(clean given pasta) + p(no pasta) * p(clean given no pasta).

that formula becomes:

the probability that she'll have a clean dress today = (2/7 * 1/2) + (5/7 * 2/3).

2/7 * 1/2 = 2/14 = 1/7

5/7 * 2/3 = 10/21

1/7 + 10/21 = 3/21 + 10/21 = 13/21.

the probability that she'll have a clean dress today is 13/21.

RELATED QUESTIONS
600 is 5/9 of what number? What percent of 50 is 40? When Merideth cleaned her room she (answered by stanbon)

Mother and Maria worked out a deal. For every day Maria walks the family dogs she gets... (answered by macston)

Bing can spend at most Php100 for his food during lunch. It cost her Php25 for a meal... (answered by ikleyn)

Jen's job pays her $15.60 per hour. If she gets a 5% raise, what will her new hourly pay... (answered by ikleyn)

Paula eats lunch at a restaurant each day, and cannot change his easily, because she... (answered by ikleyn)

A mother wishes to set up a savings account for her son's education. She plans on... (answered by ikleyn)

A mother was 21 years when she gave birth to her daughter.How old will the mother be when (answered by macston)

Every month, a girl gets allowance. Assume last year she had no money, and kept it up to... (answered by checkley75)