Back to Exercise: Understand conditional probability

Exercises: Understand the Conditional Probability of A Given B as P(A and B)/P(B)

Work through each section in order. Show your reasoning where indicated. For explanation problems, write in complete sentences. Express probabilities as fractions in lowest terms or as decimals where requested.

Grade 10·20 problems·~35 min·Common Core Math - HS Statistics and Probability·group·hss-cp-a-3

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Warm-Up: Probability Foundations

These problems review skills you already know.

From HSS.CP.A.2, two events $A$ and $B$ are independent when which equation holds?

$P(A \text{ and } B) = P(A) \cdot P(B)$

$P(A \text{ and } B) = 0$

$P(A \text{ and } B) = P(A) + P(B)$

$P(A) = P(B)$

A bag has 10 marbles: 4 red, 3 blue, 3 green. You draw one and are told it is not green. To find $P(\text{Red} \mid \text{Not Green})$ , what is the size of the restricted sample space (the outcomes you now consider)?

$10$ marbles

$7$ marbles

$4$ marbles

$3$ marbles

Given $P(A \text{ and } B) = 0.2$ and $P(B) = 0.5$ , compute $P(A \mid B) = \dfrac{P(A \text{ and } B)}{P(B)}$ .

Fluency Practice

Compute each conditional probability. Two-way tables give counts.

A class of 30 students is summarized below.

	Sports	No Sports	Total
Band	4	4	8
No Band	8	14	22
Total	12	18	30

What is $P(\text{Sports} \mid \text{Band})$ ?

$\frac{4}{8} = \frac{1}{2}$

$\frac{4}{30} = \frac{2}{15}$

$\frac{12}{30} = \frac{2}{5}$

$\frac{4}{12} = \frac{1}{3}$

For events $A$ and $B$ , $P(A) = 0.6$ , $P(B) = 0.5$ , and $P(A \text{ and } B) = 0.2$ . Compute $P(B \mid A)$ . Express your answer as a decimal.

A survey of 200 people recorded coffee and tea drinking.

	Drinks Coffee	No Coffee	Total
Drinks Tea	40	30	70
No Tea	80	50	130
Total	120	80	200

Compute $P(\text{Coffee} \mid \text{Tea})$ . Express your answer as a fraction in lowest terms.

A die is rolled. Let $A$ = "even" $= \{2,4,6\}$ and $B$ = "greater than 2" $= \{3,4,5,6\}$ . Compute $P(A \mid B)$ . Express your answer as a fraction in lowest terms.

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