Respuesta :
The probability that a randomly selected person likes cookies with chocolate or peanut butter chips is 0.77.
Step-by-step explanation:
Here, the total sample of people has total 535 people.
The percentage of people liking chocolate chip cookies = 65%
Now, 65% of 535 = [tex]\frac{65}{100} \times 535 = 347.75 \approx 348[/tex]
⇒ 348 people in total like chocolate chip cookies.
⇒ n(C) = 348
The percentage of people liking peanut butter chip cookies = 37%
Now, 37% of 535 = [tex]\frac{37}{100} \times 535 = 197.95 \approx 198[/tex]
⇒ 198 people in total like peanut butter chip cookies.
⇒ n(B) = 198
Percentage of people liking both chocolate &peanut butter chips = 25%
Now, 25% of 535 = [tex]\frac{25}{100} \times 535 =133.75 \approx 134[/tex]
⇒ 134 people in total like both chocolate &peanut butter chips
⇒ n(C ∩ B ) = 134
Now, n( C U B) = N(C) + n(B) - n(C ∩ B )
= 348 + 198 - 134 = 412
P( person likes cookies with chocolate or peanut butter chips)
= [tex]\frac{\textrm{person likes cookies with chocolate or peanut butter chips}}{\textrm{Total People}} = \frac{412}{535} = 0.77[/tex]
Hence, the probability that a randomly selected person likes cookies with chocolate or peanut butter chips is 0.77.
