Basic probability

Question 1

What is probability?

Answer 1

A measure of how likely it is that an uncertain event will occur

Question 2

How do you calculate basic probability?

Answer 2

P (event) = number of possible outcomes consistent with the event / number of possible outcomes

Question 3

Calculate the probability:

I close my eyes and role 1 die. Before I open my eyes what is the probability I have rolled an even number?

Answer 3

Even numbers on a die = 2, 4, 6 (there are 3 possible outcomes)

Numbers on a die = 1, 2, 3, 4, 5, 6 (there are 6 possible outcomes)

P = 3/6 = 1/2 = 0.5 or 50%

Question 4

What is conditional probability?

Answer 4

The probability of an event happening, given that something else is known/assumed

Question 5

Calculate conditional probability:

I close my eyes and role 1 die. An honest observer tells me that I have rolled a
number < 4. Before I open my eyes what is the probability I have rolled an even number?

Answer 5

Number < 4 on a die = 1, 2, 3 (there are 3 possible outcomes)

Number < 4 on a die that is also Even = 2 (there is only 1 possible outcome)

P = 1/3 = 0.33 or 33.33%

Question 6

Calculate the probability:

I close my eyes and role 1 fair die. Before I open my eyes what is the probability (to 2 decimal places) that I have rolled a number less than 3?

a.	0.33

b.	0.50

c.	0.67

d.	0.00

Answer 6

Number < 3 on a die = 1, 2 (there are 2 possible outcomes)

Numbers on a die = 1, 2, 3, 4, 5, 6 (there are 6 possible outcomes)

P = 2/6 = 0.33 = 33.33%

Question 7

Calculate the conditional probability

I close my eyes and roll 1 die. Before I open my eyes an honest observer tells me that I have rolled a number > 1. What is the conditional probability that I have rolled an even number given the observer’s information?

a.	0.50

b.	0.60

c.	0.33

d.	1.00

Answer 7

Number > 1 on a die = 2, 3, 4, 5, 6 (there are 5 possible outcomes)

Number > 1 on a die that is also even = 2, 4, 6 (there are 3 possible outcomes)

P = 3/5 = 0.60 = 60%
Answer = B

Question 8

I close my eyes and roll 1 die.

A) What is the probability I have rolled an even number that is > 5? (to 2 d.p.)

B) Before I open my eyes an honest observer tells me that I have rolled a number > 5. What is the conditional probability that I have rolled an even number given the observer’s information? (to 2 d.p.)

a.	A) 0.50  B) 0.50

b.    A) 1.00.  B) 1.00

c.	A) 0.17  B) 1.00

d.	A) 0.17  B) 0.17

Answer 8

A) Even number that is > 5 on a die = 6 (there is only 1 possible outcome)

P = 1/6 = 0.17

B) Number > 5 on a die = 6 (there is only 1 possible outcome)

Number > 5 that is even = 6 (there is only 1 possible outcome)

P = 1/1 = 1.00

Answer = C