Real estate suggests that 91% of homes for sale have garages (let it be an event A), 14% have swimming pools (let it be an event B) , and 10% have both features: a garage and a pool.

d) Are events A and B independent?

(Hint: No verbal reasoning please, we should just check whether our data fit the (mathematical!) definitionof independence. To this end, you should provide a half-minute calculation.)

Question 13 options:

Yes

No

On vacations, Ann travels either to North or to South from her home. Each time, to choose where to go, she rolls a die. If the dieshows an even number, Ann travels to North. If the die shows an odd number, she travels to South.

Suppose thatthe probability that there will be rainy on vacation in North is 0.4, while for South the same probability is 0.2.

a)Find the probability that it will be rainy on vacation. (Hint: you should grapha tree.)

Question 14 options:

0.3

0.2

0.4

0.5

On vacations, Ann travels either to North or to South from her home. Each time, to choose where to go, she rolls a die. If the dieshows an even number, Ann travels to North. If the die shows an odd number, she travels to South.

Suppose thatthe probability that there will be rainy on vacation in North is 0.4, while for South the same probability is 0.2.

b)Let us consider theconditionalprobability that it was rainygiventhat Ann travelled too South. Not calculating anything, just say whether you expectthis probabilityto be smaller than 0.5, or larger than 0.5, or equal to 0.5. (Hint:You may (and should) proceed just from common sense.)

Question 15 options:

Equal

Larger

Smaller

On vacations, Ann travels either to North or to South from her home. Each time, to choose where to go, she rolls a die. If the dieshows an even number, Ann travels to North. If the die shows an odd number, she travels to South.

Suppose thatthe probability that there will be rainy on vacation in North is 0.4, while for South the same probability is 0.2.

c) Compute the probability defined in the previous Question 15. (Hint: We are dealing with a conditional probability.)

Question 16 options:

1/2

1/3

2/3

0.1