Task Sets: Understand conditional probability - Common Core Math - HS Statistics and Probability

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.

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

Warm-Up: Probability Foundations

Fluency Practice