Question

question 7
a and b are independent events.
$p(a) = 0.50$
$p(b) = 0.30$
what is $p(a|b)$?
a. not enough information
b. 0.50
c. 0.15
d. 0.30

question 8
at a store, the probability that a customer buys socks is 0.15. the probability that a customer buys socks given that the customer buys shoes is 0.20.
which statement is true?
a. buying socks and buying shoes are dependent events.
b. the probability that a customer buys socks and shoes is 0.05.
c. buying socks and buying shoes are independent events.
d. every customer who buys shoes also buys socks.

question 9
on the planet kudzu, the probability that a bird is green is 0.30. the probability that the bird is green given that the bird is female is 0.30.
which statement is true?
a. the probability that a bird on kudzu is female and green is 0.30.
b. on kudzu, being female and being green are dependent events.
c. on kudzu, being female and being green are independent events.
d. all of the female birds on kudzu are green.

question 10
in littletown, the probability that a baseball team goes to the city playoffs is 0.30. the probability that the team goes to the state playoffs given that the team goes to the city playoffs is 0.20.
what is the probability that a randomly selected team from littletown goes to the city and state playoffs?
a. 0.10
b. 0.06
c. 0.66
d. 0.50

Explanation:

Question 7

Step1: Recall independent events rule

For independent events, $P(A|B) = P(A)$

Step2: Substitute given value

$P(A|B) = 0.50$

Question 8

Step1: Define events

Let $S$ = buy socks, $Sh$ = buy shoes. Given $P(S)=0.15$, $P(S|Sh)=0.20$

Step2: Check independence condition

Events are independent if $P(S|Sh)=P(S)$. Since $0.20
eq 0.15$, events are dependent.

Question 9

Step1: Define events

Let $G$ = bird is green, $F$ = bird is female. Given $P(G)=0.30$, $P(G|F)=0.30$

Step2: Check independence condition

Events are independent if $P(G|F)=P(G)$. Since $0.30 = 0.30$, events are independent.

Question 10

Step1: Recall conditional probability formula

$P(\text{city and state}) = P(\text{state|city}) \times P(\text{city})$

Step2: Substitute given values

$P(\text{city and state}) = 0.20 \times 0.30 = 0.06$

Answer:

Question 7: B. 0.50
Question 8: A. Buying socks and buying shoes are dependent events.
Question 9: C. On Kudzu, being female and being green are independent events.
Question 10: B. 0.06