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ou have a plate of 40 cookies. Ten have chocolate chips and 15 have pecans, Of the cookies mentioned in the preceding
entence, nine have both chocolate chips and pecans. You select a cookie at random. What is the probability that your coo
hocolate chips or pecans?
Express numbers in exact form. Use symbolic notation and fractions where needed.)
probability your cookie has chocolate chips or pecans:

Ask by Bolton Flynn. in the United States
Mar 29,2025

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The probability that a randomly selected cookie has chocolate chips or pecans is .

Solución

Let be the event that a cookie has chocolate chips and the event that a cookie has pecans.
  1. The number of cookies with chocolate chips is .
  2. The number of cookies with pecans is .
  3. The number of cookies with both is .
Using the formula for the union of two sets, the total number of cookies with chocolate chips or pecans is
Since there are cookies in total, the probability that a randomly selected cookie has chocolate chips or pecans is

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Mind Expander

To find the probability that a randomly selected cookie has chocolate chips or pecans, we can use the formula for the probability of the union of two events:
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
Here, let A be the event that a cookie has chocolate chips, and B be the event that a cookie has pecans.
  • P(A) (cookies with chocolate chips) = 10/40
  • P(B) (cookies with pecans) = 15/40
  • P(A ∩ B) (cookies with both chocolate chips and pecans) = 9/40
Now substituting into the formula:
P(A ∪ B) = (10/40) + (15/40) - (9/40) = (10 + 15 - 9) / 40 = 16/40 = 2/5.
So, the probability that your cookie has chocolate chips or pecans is 2/5.
To sum it all up, the chances of biting into a cookie with these nutty delights? Well, you have a solid 2 out of 5 chances!

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