Question

In a random sample of 535 people 65% said they like cookies with chocolate chips 37% like cookies with peanut butter chips. 25% like cookies with both chocolate and peanut butter chips. What is the probability that a randomly selected person likes cookies with chocolate or peanut butter chips

Answer 1

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   = $\frac{65}{100} \times 535 = 347.75 \approx 348$

⇒ 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   = $\frac{37}{100} \times 535 = 197.95 \approx 198$

⇒ 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   = $\frac{25}{100} \times 535 =133.75 \approx 134$

⇒ 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)  

= $\frac{\textrm{person likes cookies with chocolate or peanut butter chips}}{\textrm{Total People}} = \frac{412}{535} = 0.77$

Hence, the probability that a randomly selected person likes cookies with chocolate or peanut butter chips is 0.77.