Free Dependent and independent events Practice Problems • Learn To Be

Anwar selects a playing card at random from the following

6

cards:

\{

9

of hearts,

5

of spades,

6

of hearts,

2

of spades,

4

of hearts,

7

of hearts

\}

Let

A

be the event that Anwar selects an even-numbered card and

B

be the event that she chooses a heart.

Which of the following statements are true?

Choose all answers that apply:

A
$P(A\text{ | }B)=P(A)$ , the conditional probability that Anwar selects an even-numbered card given that she has chosen a heart is equal to the probability that Anwar selects an even-numbered card.
B
$P(B\text{ | }A)=P(B)$ , the conditional probability that Anwar selects a heart given that she has chosen an even-numbered card is equal to the probability that Anwar selects a heart.
C
Events $A$ and $B$ are independent events.
D
The outcome of events $A$ and $B$ are dependent on each other.
E
$P(A\text{ and }B)=P(A) \cdot P(B)$ , the probability that Anwar selects a card that is even-numbered and a heart is equal to the probability that Anwar selects an even-numbered card multiplied by the probability that she selects a heart.

Dependent and independent events