12 multiple-choice questions, progressively harder.
A fair die is rolled once. What is the probability of rolling a 444?
Solution
Correct answer: B
The die has 666 equally likely faces, and exactly one of them is a 444, so there is 111 favorable outcome out of 666.
P(4)=16P(4) = \frac{1}{6}P(4)=61
Every single face of a fair die has this same probability.
Which probability describes an event that is impossible?
Correct answer: D
Probability runs from 000 to 111. The bottom of the scale means the event can never happen.
P(impossible)=0P(\text{impossible}) = 0P(impossible)=0
A probability of 111 (or 100%100\%100%) is the opposite end, a certain event.
The fair spinner shown has 444 equal sectors, and 111 is shaded. What is the probability of landing on the shaded sector?
Correct answer: A
The sectors are equal, so the 444 sectors are equally likely. One of them is shaded.
P(shaded)=14P(\text{shaded}) = \frac{1}{4}P(shaded)=41
Equal sectors are what let you count this way.
A fair die is rolled once. What is the probability of rolling a number greater than 444?
Correct answer: C
The numbers greater than 444 are {5,6}\{5, 6\}{5,6}, which is 222 favorable outcomes out of 666.
P(>4)=26=13P(>4) = \frac{2}{6} = \frac{1}{3}P(>4)=62=31
Reduce 26\frac{2}{6}62 to 13\frac{1}{3}31.
A fair coin is flipped once. What is the probability that it lands tails?
A flip has two equally likely outcomes, heads and tails, and one of them is tails.
P(tails)=12P(\text{tails}) = \frac{1}{2}P(tails)=21
The two sides share the one whole equally.
A fair die is rolled once. What is the probability of rolling an odd number?
The odd faces are {1,3,5}\{1, 3, 5\}{1,3,5}, which is 333 favorable outcomes out of 666.
P(odd)=36=12P(\text{odd}) = \frac{3}{6} = \frac{1}{2}P(odd)=63=21
Half the faces are odd, so the probability is 12\frac{1}{2}21.
A bag holds 333 red, 222 yellow, and 555 blue marbles. You draw one at random. What is the probability it is blue?
The bag holds 3+2+5=103 + 2 + 5 = 103+2+5=10 marbles, all equally likely, and 555 of them are blue.
P(blue)=510=12P(\text{blue}) = \frac{5}{10} = \frac{1}{2}P(blue)=105=21
Reduce 510\frac{5}{10}105 to 12\frac{1}{2}21.
A fair die is rolled once. Which event is more likely, rolling an even number or rolling a 555?
Rolling an even number has 333 favorable faces {2,4,6}\{2, 4, 6\}{2,4,6}, while rolling a 555 has only 111.
P(even)=36=12andP(5)=16P(\text{even}) = \frac{3}{6} = \frac{1}{2} \quad\text{and}\quad P(5) = \frac{1}{6}P(even)=63=21andP(5)=61
Since 12\frac{1}{2}21 is larger than 16\frac{1}{6}61, the even number is more likely.
A fair die is rolled once. What is the probability of rolling a number that is 666 or less?
Every face of the die (111 through 666) is 666 or less, so all 666 outcomes are favorable.
P(≤6)=66=1P(\le 6) = \frac{6}{6} = 1P(≤6)=66=1
An event that always happens has probability 111, certain.
A fair spinner has 555 equal sectors, 111 of them red. What is the probability of landing on red?
Equal sectors are equally likely, so there are 555 equally likely outcomes, 111 of them red.
P(red)=15P(\text{red}) = \frac{1}{5}P(red)=51
One sector out of five is favorable.
A bag holds 666 marbles, of which 222 are green. You draw one at random. What is the probability it is green?
There are 666 equally likely marbles and 222 of them are green.
P(green)=26=13P(\text{green}) = \frac{2}{6} = \frac{1}{3}P(green)=62=31
A bag holds 333 red and 777 blue marbles. You draw one at random. What is the probability it is not red?
The bag holds 3+7=103 + 7 = 103+7=10 marbles. Not red means blue, and there are 777 blue.
P(not red)=710P(\text{not red}) = \frac{7}{10}P(not red)=107
The complement rule agrees: 1−310=7101 - \frac{3}{10} = \frac{7}{10}1−103=107.
Reset this practice set?
This clears every answer you have given and starts the set again from question 1.