Numberphile

PROBABILITY QUESTIONS WITH SOLUTIONS

Question 1

A die is rolled, find the probability that an even number is obtained

Let us first write the sample space S of the experiment

S = {1,2,3,4,5,6}
Let E be the event "an even number is obtained" and write it down

E = {2,4,6}

We now use the formula of the classical probability

P(E) = n(E) / n(S) = 3 / 6 = 1 / 2

Question 2

Two coins are tossed, find the probability that two heads are obtained

Note: Each coin has two possible outcomes H (heads) and T (Tails)

The sample space S is given by

S = {(H,T),(H,H),(T,H),(T,T)}
Let E be the event "two heads are obtained"

E = {(H,H)}

We use the formula of the classical probability

P(E) = n(E) / n(S) = 1 / 4

Question 3

Which of these numbers cannot be a probability?

a) -0.00001
b) 0.5
c) 1.001
d) 0
e) 1
f) 20%

A probability is always greater than or equal to 0 and less than or equal to 1, hence only a) and c) above cannot represent probabilities: -0.00010 is less than 0 and 1.001 is greater than 1

Question 4

a) A die is rolled, find the probability that the number obtained is greater than 4.

b) Two coins are tossed, find the probability that one head only is obtained.

c) Two dice are rolled, find the probability that the sum is equal to 5.

d) A card is drawn at random from a deck of cards. Find the probability of getting the King of heart

Answers:

a) 2 / 6 = 1 / 3

b) 2 / 4 = 1 / 2

c) 4 / 36 = 1 / 9

d) 1 / 52

Question 5

A card is drawn at random from a deck of cards. Find the probability of getting the 3 of diamond