PROBABILITY

Statistic Problems - Probability

Statistic Problems - Probability

Answer No. 1

Probability of winning ticket will be greater than 7

=

20

=

0.741

27

Answer No. 2

Data

Probability of Second Home

Probability of Not having the second home

0.31

0.69

Probability of Income over 100000 euros

Probability of not having income over 100000 euros

0.21

0.79

Probability of second home and income

Probability of not having second home and income

0.06

0.94

Solution

a) Therefore, it can be said that probability that a randomly selected person does not have a second home is 0.69.

b) Therefore, it can be said that probability that a randomly selected person must pay this new flat tax rate is 0.21 + 0.06 = 0.27.

Answer No. 3

If A is the event that makes a claim and B is the event that age of insured is under 25.

Probability of Claim

Probability of Do not claim

21

=

0.8400

4

=

0.1600

25

25

Probability of age under 25

Probability of age is not under 25

21

=

0.3750

4

=

0.0714

56

56

a) Therefore, it can be said that the probability that a random person makes a claim P (A) = 0.8400

b) Therefore, it can be said that the probability that a random person from the sample is under 25 and makes a claim P (A) = 0.3750

c) Given the random selected person is under 25 and the probability that the person makes a claim;

P (A | B) =

0.3750

=

0.4464

0.8400

Answer No. 4

b) From the question 3, it can be said that, Yes, events "age category 2" and "makes a claim" because P ("age category 2" and "claim") = 0

Answer No. 5

The events "A" and "B" described in question 3 are independent events:

d) Yes, because P ("claim" | "age category 1") = P ("claim")

Answer No. 6

Data

0

1

2

3

0.29

0.24

0.16

?

Solution

a) The missing probability, P (X = 3) = 1 - 0.29 - 0.24 - 0.16 = 0.31

0

1

2

3

0.29

0.24

0.16

0.31

b) P (X = 2) = 0.16 + 0.31 = 0.47

c) P (X <= 2) = 0.29 + 0.24 + 0.16 = 0.69

d)

X = ...