oliver looked at some boxes of cereal in the grocery store. for each one, he recorded the size and whether…

oliver looked at some boxes of cereal in the grocery store. for each one, he recorded the size and whether or not it contained a prize.\n| | prize | no prize |\n|--|--|--|--|\n| mini size | 9 | 6 |\n| regular size | 5 | 9 |\n| jumbo size | 7 | 8 |\nwhat is the probability that a randomly selected box of cereal is jumbo size given that the box of cereal contains a prize?\nsimplify any fractions.

oliver looked at some boxes of cereal in the grocery store. for each one, he recorded the size and whether or not it contained a prize.\n| | prize | no prize |\n|--|--|--|--|\n| mini size | 9 | 6 |\n| regular size | 5 | 9 |\n| jumbo size | 7 | 8 |\nwhat is the probability that a randomly selected box of cereal is jumbo size given that the box of cereal contains a prize?\nsimplify any fractions.

Answer

Explanation:

Step1: Calculate total boxes with prize

Add the number of boxes with a prize in each size category. $9 + 5+7=21$.

Step2: Calculate number of jumbo - sized boxes with prize

The number of jumbo - sized boxes with a prize is 7.

Step3: Calculate conditional probability

The formula for conditional probability $P(A|B)=\frac{P(A\cap B)}{P(B)}$. In this case, the probability that a box is jumbo - sized given it contains a prize is the number of jumbo - sized boxes with a prize divided by the total number of boxes with a prize. So the probability is $\frac{7}{21}=\frac{1}{3}$.

Answer:

$\frac{1}{3}$