Respuesta :
The probability that the pink jar was chosen, when it is known that the cookie was a sugar cookie is 0.167..
What is Bayes' theorem?
Suppose that there are two events A and B. Then suppose the conditional probability are:
P(A|B) = probability of occurrence of A given B has already occurred.
P(B|A) = probability of occurrence of B given A has already occurred.
There are three colored cookie jars. One jar is blue, another green and the last one pink.
- The blue jar contains 10 chocolate chip and 7 sugar cookies.
- The green jar contains 8 chocolate chip, 14 sugar and 11 peanut butter cookies.
- The pink jar contains 6 chocolate chip, 5 sugar and 9 peanut butter cookies.
Thus the probability of chossing sugar is,
[tex]P=\dfrac{1}{2}\times\dfrac{7}{17}+\dfrac{1}{4}\times\dfrac{17}{33}+\dfrac{1}{4}\times\dfrac{5}{20}[/tex]
One of the three cookie jars is chosen at random. The probabilities that the blue jar, green jar, or pink jar will be chosen are 1⁄2 , 1⁄4 , and 1⁄4 , respectively.
Thus the probability for pink jar was chosen, when it is known that the cookie was a sugar cookie is,
[tex]\rm P=\dfrac{P(pink\cap sugar)}{P(sugar)}\\\rm P=\dfrac{P(sugar| pink)P(Pink)}{P(sugar)}[/tex]
Put the values,
[tex]P=\dfrac{\dfrac{1}{4}\times\dfrac{5}{20}}{\dfrac{1}{2}\times\dfrac{7}{17}+\dfrac{1}{4}\times\dfrac{17}{33}+\dfrac{1}{4}\times\dfrac{5}{20}}\\P=0.167[/tex]
Thus, the probability that the pink jar was chosen, when it is known that the cookie was a sugar cookie is 0.167.
Learn more about the Bayes' theorem here;
https://brainly.com/question/13750253
