find the probability that a writing utensil is red, given it is a pencil.\n| | red | green | blue | total…

find the probability that a writing utensil is red, given it is a pencil.\n| | red | green | blue | total |\n|--|--|--|--|--|\n| marker | 12 | 5 | 14 | 31 |\n| pencil | 9 | 6 | 7 | 22 |\n| crayon | 7 | 8 | 6 | 21 |\n| total | 28 | 19 | 27 | 74 |\nnext, find the probability of a writing utensil being a pencil.\np(pencil) = \\frac{?}{74}

find the probability that a writing utensil is red, given it is a pencil.\n| | red | green | blue | total |\n|--|--|--|--|--|\n| marker | 12 | 5 | 14 | 31 |\n| pencil | 9 | 6 | 7 | 22 |\n| crayon | 7 | 8 | 6 | 21 |\n| total | 28 | 19 | 27 | 74 |\nnext, find the probability of a writing utensil being a pencil.\np(pencil) = \\frac{?}{74}

Answer

Explanation:

Step1: Calculate conditional probability

The formula for conditional probability $P(A|B)=\frac{P(A\cap B)}{P(B)}$. Here, $A$ is the event that the writing - utensil is red and $B$ is the event that the writing - utensil is a pencil. The number of red pencils is 9 and the number of pencils is 22. So the probability that a writing utensil is red, given it is a pencil is $P(\text{red}|\text{pencil})=\frac{9}{22}$.

Step2: Calculate probability of being a pencil

The total number of writing utensils is 74 and the number of pencils is 22. So $P(\text{pencil})=\frac{22}{74}$.

Answer:

The probability that a writing utensil is red, given it is a pencil is $\frac{9}{22}$. The probability of a writing utensil being a pencil is $\frac{22}{74}$.