Odds
What are the odds of rolling a 3 on a six-sided die?
Odds = 1 favorable outcome (rolling a 3) / 5 unfavorable outcomes (not rolling a 3) → Odds = 1:5
A box contains 3 red, 5 blue, and 2 green marbles. What is the probability of drawing a red marble?
Total marbles = 3 + 5 + 2 = 10
Probability of red = 3/10 → Probability = 0.3 or 30%
If you roll a die, what is the expected value of the roll?
EV = (1+2+3+4+5+6) / 6 = 21 / 6 → Expected value = 3.5
A card is drawn from a deck of 52 cards. What is the probability of drawing a King?
There are 4 Kings in a deck of 52 cards.
Probability = 4/52 → Probability = 1/13 or ~7.69%
Given that it is raining, what is the probability that you will need an umbrella?
This is a conditional probability question. If it's raining, the probability you need an umbrella is close to 1 (almost certain).
A die is rolled. What are the odds in favor of rolling a number greater than 4?
Numbers greater than 4 are 5 and 6. There are 2 favorable outcomes and 4 unfavorable outcomes (1, 2, 3, 4).
Odds in favor = 2:4 → Odds = 1:2
A spinner has 5 equal sections: 1 red, 2 green, and 2 blue. What is the probability of landing on green?
Probability of landing on green = 2/5 → Probability = 0.4 or 40%
If you roll a die, what is the expected value of rolling a 4, 5, or 6?
The outcomes 4, 5, and 6 are favorable, so EV = (4+5+6) / 3 = 15 / 3 → Expected value = 5
What is the theoretical probability of rolling an even number on a six-sided die?
The even numbers on a die are 2, 4, and 6.
Probability = 3/6 → Probability = 1/2 or 50%
You pick two cards from a deck without replacement. What is the probability that both cards are spades?
Probability of drawing the first spade = 13/52.
Probability of drawing the second spade = 12/51 (since one spade was already drawn).
Probability = (13/52) * (12/51) → Probability = 1/17 or ~5.88%
What are the odds of drawing a red card from a deck of cards?
There are 26 red cards (13 hearts and 13 diamonds) in a deck of 52.
Odds of drawing red = 26:52 → Odds = 1:2
What is the probability of flipping a coin and getting tails?
The probability of tails on a fair coin = 1/2 → Probability = 0.5 or 50%
You have a cone with a radius of 4 cm and a height of 9 cm. What is the volume of the cone? Use π ≈ 3.14.
Volume=1/3πr2h
150.72cm3
A die is rolled. What is the probability of rolling a number less than 4?
The favorable outcomes are 1, 2, and 3.
Probability = 3/6 → Probability = 1/2 or 50%
A cone has a radius of 6 cm and a slant height of 10 cm. What is the surface area?
Surface Area=πrl+πr2
301.44 cm2
A cube has a side length of 6 meters. What is the surface area of the cube?
Surface Area=6×side2 Surface Area=6×62=6×36=216m2
A box has 4 black balls, 3 white balls, and 1 red ball. What is the probability of drawing a white ball?
Probability of drawing a white ball = 3/8 → Probability = 0.375 or 37.5%
mill1ion
One in a million
A survey of 100 students finds that 30 prefer coffee over tea. What is the empirical probability of selecting a coffee drinker?
Empirical probability = 30/100 → Probability = 0.3 or 30%
R+R+R
Summer
A cone has a radius of 6 cm and a slant height of 10 cm. What is the volume of the cone?
Volume=1/3πr2h
301.44cm3
A jar contains 3 red, 4 blue, and 5 yellow marbles. What is the probability of drawing a yellow marble?
Total marbles = 3 + 4 + 5 = 12
Probability of drawing a yellow marble = 5/12 → **Probability = 0.4167
10AC
Tennessee
This is the formula for the volume of a rectangular prism.
What is length × width × height?
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Tennis shoes