Say someone has made a 4-sided die, and states the following probabilities of getting a side (1,2,3, or 4). In each part, state whether a proper probability distribution was used. Why or why not.

a. P(1) = 0.25, P(2) = −0.1, P(3) = 0.35, P(4) = 0.25
b. P(1) = 0.25, P(2) = 0.25, P(3) = 0.25, P(4) = 0.25
c. P(1) = 0.25, P(2) = 0.1, P(3) = 0.35, P(4) = 0.25

(a) NOT proper probability distribution was used

(b) Proper probability probality d

(c) NOT proper probability distribution was used .

Step-by-step explanation:

Probability is a measure of likeliness of an event.

A four-sided dies with faces 1, 2, 3 and 4, when rolled (without bias) is likely of turning 1, or 2, or 3, or 4. Every of its faces are equally likely to turn.

Now, the probability of success plus the probability of failure of an event is always equal to one.

This makes it reasonable that the probability of success or failure of an event is less or equal to one. And the probability of an event is pro

Now, when the die is rolled, there are four possible outcomes, 1 or 2 or 3 or 4.

Probability of 1 = 1/4 = 0.25

Probability of 2 = 1/4 = 0.25

Probability of 3 = 1/4 = 0.25

Probability of 4 = 1/4 = 0.25

(a) The results P(1) = -0.1, is unrealistic, as the probability of success or failure of an event is never less than 0. So, a wrong probability distribution was used.

(b) This reflects what was explained, so, it used the proper probability distribution. It is the correct option.

(c) There is no reason for the probabilities of these events to differ from each other. So, the wrong probability distribution was used.

step-by-step explanation:

x^2 -12x + 36 + y^2 = 36

x^2 + y^2 = 12x

r^2 = 12rcos(theta)

r = 12 cos(theta)