BASICS AND RULES
A probability based on a personal judgement or experience is called this type of probability.
Subjective probability
Express the odds in favour of rolling a sum of 3 on two dice.
1:17
A 4 digit PIN is formed using digits 0-9 without repetition. What is the probability that the first digit is 7?
1/10
A coin is flipped and a dice is rolled. Determine the probability of landing on heads and rolling a 1.
(1/2)(1/6)=1/12
Create an example where two events are NON-mutually exclusive.
Rolling doubles, rolling a sum of 4.
If P(A)=0.35, determine P(A')
0.65
The odds against winning a game are 3:2. Determine the probability of winning.
2/5
Six students line up randomly. What is the probability that person A and person B are beside each other.
(2 x 5!)/6! = 1/3
Two cards are drawn with replacement. What is the probability that the two cards drawn are 5s?
P(both 5s)
= 4/52 * 4/52
= 1/13 * 1/13
=1/169 or 0.59%
A single card is drawn from a standard deck of 52 cards. What is the probability of drawing a king or a queen? Explain why the events are mutually exclusive.
4/52 + 4/52 = 2/13
Give an example of two events that are independent.
Tossing two coins, rolling 2 dices, drawing two cards with replacement.
The odds in favour of an event are 7:5. Determine the probability that the event does not occur.
5/12
There are 5 blue marbles, 4 green and 1 red marble. If you draw 2 marbles at the same time, what is the probability that at least one is green?
1 - 6C2/10C2 = 0.67
A bag contains 4 red, 5 blue and 3 green marbles. Two are selected without replacement. What is the probability that both are blue?
(5/12)(4/11) = 5/33
If P(A)=0.4 and P(B)=0.5, and A and B are mutually exclusive, determine P(A or B).
0.9
A card is drawn from a standard deck. Determine the probability that it is a heart or a face card.
22/52 = 11/26
A bag contains red, blue and green marbles. The odds in favour of selecting a red marble are 2:5. If there are 15 non-red marbles, how many red marbles are there?
6 red marbles.
Five cards are dealt from a standard deck. What is the probability of getting exactly 2 aces?
0.0399
In a class of 30 students, 18 play soccer, 12 play basketball, and 7 play both. Given that the student plays soccer, what is the probability they also play basketball?
P(Basketball | Soccer) = (7/30) / (18/30) = 7/18
If P(A)=0.6, P(B)=0.4 and P(A and B)=0.2, determine P(A U B).
0.8
A basketball player makes 42 out of 60 free throws. Determine the expected number of shots he makes if he makes 1000 free throws.
700
The odds against winning a carnival game are 7:3. If a player plays the game twice, what is the probability that they win exactly twice?
P(win twice)
= 3/10 * 3/10
=9/100 or 9%
A group of 5 is selected from 7 girls and 6 boys. What is the probability of selecting at least 3 girls.
84/143 = 0.587
Has a job No job Total
Plays a sport 35 25 60
Does not play sport 15 45 60
Total 50 70 120
If a randomly selected student does not have a part time job, what is the probability that they play a sport?
P(Sport | no job)
= 25/70
=5/14 or 35.7%
Events A and B are mutually exclusive. The probability of A occurring is 0.35, and the probability of neither A NOR B occurring is 0.2. Determine the probability of event B.
P(A U B) = 1-0.2 = 0.8
0.8 = P(A) + P(B)
0.8 = 0.35 + P(B)
0.45 = P(B)