Probability - SAT Math
Card 0 of 41
A bag has 3 red, 2 blue marbles. On a single draw, what is: $P(\text{red})$?
A bag has 3 red, 2 blue marbles. On a single draw, what is: $P(\text{red})$?
Tap to see back →
$\frac{3}{5}$.
$\frac{3}{5}$.
A box has 4 red and 6 blue marbles. Find $P(\text{blue then red})$ without replacement.
A box has 4 red and 6 blue marbles. Find $P(\text{blue then red})$ without replacement.
Tap to see back →
$\frac{6}{10}\times\frac{4}{9}=\frac{4}{15}$.
$\frac{6}{10}\times\frac{4}{9}=\frac{4}{15}$.
Complement probability of no heads in 3 flips.
Complement probability of no heads in 3 flips.
Tap to see back →
$1-\frac{1}{8}=\frac{7}{8}$.
$1-\frac{1}{8}=\frac{7}{8}$.
Expected value definition.
Expected value definition.
Tap to see back →
Weighted average of all possible outcomes by probability.
Weighted average of all possible outcomes by probability.
Find $P(\text{blue then red})$ with replacement.
Find $P(\text{blue then red})$ with replacement.
Tap to see back →
$\frac{6}{10}\times\frac{4}{10}=\frac{6}{25}$.
$\frac{6}{10}\times\frac{4}{10}=\frac{6}{25}$.
If $P(A)=0.3$ and $P(B|A)=0.5$, find $P(A \text{ and } B)$.
If $P(A)=0.3$ and $P(B|A)=0.5$, find $P(A \text{ and } B)$.
Tap to see back →
$0.15$.
$0.15$.
If $P(A)=0.3$, $P(B)=0.6$, independent events, find $P(A \text{ and } B)$.
If $P(A)=0.3$, $P(B)=0.6$, independent events, find $P(A \text{ and } B)$.
Tap to see back →
$0.18$.
$0.18$.
If $P(A)=0.4$, $P(B)=0.3$, independent, find $P(\text{not A and B})$.
If $P(A)=0.4$, $P(B)=0.3$, independent, find $P(\text{not A and B})$.
Tap to see back →
$(1-0.4)\times0.3=0.18$.
$(1-0.4)\times0.3=0.18$.
If $P(A)=0.4$, $P(B)=0.5$, $P(A \text{ and } B)=0.2$, find $P(A \text{ or } B)$.
If $P(A)=0.4$, $P(B)=0.5$, $P(A \text{ and } B)=0.2$, find $P(A \text{ or } B)$.
Tap to see back →
$0.4+0.5-0.2=0.7$.
$0.4+0.5-0.2=0.7$.
If a coin if flipped twice, what is $P(\text{at least one head})$?
If a coin if flipped twice, what is $P(\text{at least one head})$?
Tap to see back →
$1-(\frac{1}{2})^2=\frac{3}{4}$.
$1-(\frac{1}{2})^2=\frac{3}{4}$.
If two fair dice are rolled, what is $P(\text{both even})$?
If two fair dice are rolled, what is $P(\text{both even})$?
Tap to see back →
$\frac{9}{36}=\frac{1}{4}$.
$\frac{9}{36}=\frac{1}{4}$.
If two fair dice are rolled, what is $P(\text{sum}=7)$?
If two fair dice are rolled, what is $P(\text{sum}=7)$?
Tap to see back →
$\frac{6}{36}=\frac{1}{6}$.
$\frac{6}{36}=\frac{1}{6}$.
In 3 coin flips, $P(\text{exactly 2 heads})$.
In 3 coin flips, $P(\text{exactly 2 heads})$.
Tap to see back →
$\frac{3}{8}$.
$\frac{3}{8}$.
Independent events meaning.
Independent events meaning.
Tap to see back →
Outcome of one does not affect the other.
Outcome of one does not affect the other.
Mutually exclusive events meaning.
Mutually exclusive events meaning.
Tap to see back →
Cannot happen at the same time.
Cannot happen at the same time.
Number of outcomes flipping 3 coins.
Number of outcomes flipping 3 coins.
Tap to see back →
$2^3=8$.
$2^3=8$.
Number of outcomes when rolling two dice.
Number of outcomes when rolling two dice.
Tap to see back →
$6\times6=36$.
$6\times6=36$.
Probability of at least one tail in 2 flips.
Probability of at least one tail in 2 flips.
Tap to see back →
$1-\frac{1}{4}=\frac{3}{4}$.
$1-\frac{1}{4}=\frac{3}{4}$.
Probability of drawing a red card from a deck.
Probability of drawing a red card from a deck.
Tap to see back →
$\frac{26}{52}=\frac{1}{2}$.
$\frac{26}{52}=\frac{1}{2}$.
Probability of drawing an ace from a deck.
Probability of drawing an ace from a deck.
Tap to see back →
$\frac{4}{52}=\frac{1}{13}$.
$\frac{4}{52}=\frac{1}{13}$.
Probability of exactly one head in 2 flips.
Probability of exactly one head in 2 flips.
Tap to see back →
$\frac{2}{4}=\frac{1}{2}$.
$\frac{2}{4}=\frac{1}{2}$.
Probability of flipping heads on one coin.
Probability of flipping heads on one coin.
Tap to see back →
$\frac{1}{2}$.
$\frac{1}{2}$.
Probability of neither A nor B.
Probability of neither A nor B.
Tap to see back →
$1-P(A \text{ or } B)$.
$1-P(A \text{ or } B)$.
Probability of no heads in three coin flips.
Probability of no heads in three coin flips.
Tap to see back →
$(\frac{1}{2})^3=\frac{1}{8}$.
$(\frac{1}{2})^3=\frac{1}{8}$.
Probability of rolling a 6 then a 6.
Probability of rolling a 6 then a 6.
Tap to see back →
$(\frac{1}{6})^2=\frac{1}{36}$.
$(\frac{1}{6})^2=\frac{1}{36}$.
Probability of rolling a number greater than 4 on one die.
Probability of rolling a number greater than 4 on one die.
Tap to see back →
$\frac{2}{6}=\frac{1}{3}$.
$\frac{2}{6}=\frac{1}{3}$.
Probability of rolling an odd number on one die.
Probability of rolling an odd number on one die.
Tap to see back →
$\frac{3}{6}=\frac{1}{2}$.
$\frac{3}{6}=\frac{1}{2}$.
Probability of rolling even then odd.
Probability of rolling even then odd.
Tap to see back →
$\frac{1}{2}\times\frac{1}{2}=\frac{1}{4}$.
$\frac{1}{2}\times\frac{1}{2}=\frac{1}{4}$.
Probability of selecting a letter from 'SAT' that is a vowel.
Probability of selecting a letter from 'SAT' that is a vowel.
Tap to see back →
$\frac{1}{3}$.
$\frac{1}{3}$.
Probability of selecting a vowel from English alphabet.
Probability of selecting a vowel from English alphabet.
Tap to see back →
$\frac{5}{26}$.
$\frac{5}{26}$.
Probability of two independent events both happening.
Probability of two independent events both happening.
Tap to see back →
Multiply their probabilities.
Multiply their probabilities.
Sum of probabilities of all possible outcomes.
Sum of probabilities of all possible outcomes.
Tap to see back →
1
1
What is the addition rule for mutually exclusive events?
What is the addition rule for mutually exclusive events?
Tap to see back →
$P(A \text{ or } B) = P(A) + P(B)$.
$P(A \text{ or } B) = P(A) + P(B)$.
What is the conditional probability formula?
What is the conditional probability formula?
Tap to see back →
$P(A|B)=\frac{P(A \text{ and } B)}{P(B)}$.
$P(A|B)=\frac{P(A \text{ and } B)}{P(B)}$.
What is the formula for complementary probability?
What is the formula for complementary probability?
Tap to see back →
$P(\text{not A}) = 1 - P(A)$.
$P(\text{not A}) = 1 - P(A)$.
What is the formula for probability of 'at least one' event?
What is the formula for probability of 'at least one' event?
Tap to see back →
$1 - P(\text{none})$.
$1 - P(\text{none})$.
What is the fundamental counting principle?
What is the fundamental counting principle?
Tap to see back →
Multiply the number of outcomes for each stage.
Example: if a restaurant offers a choice of 3 sandwiches, 2 sides, and 4 drinks in its value meals, multiply 3 x 2 x 4 to see 24 total value meal combinations.
Multiply the number of outcomes for each stage.
Example: if a restaurant offers a choice of 3 sandwiches, 2 sides, and 4 drinks in its value meals, multiply 3 x 2 x 4 to see 24 total value meal combinations.
What is the general addition rule in probability?
What is the general addition rule in probability?
Tap to see back →
$P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)$.
$P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)$.
What is the general formula for probability of a favorable outcome?
What is the general formula for probability of a favorable outcome?
Tap to see back →
$P(A)=\frac{\text{favorable outcomes}}{\text{total outcomes}}$.
$P(A)=\frac{\text{favorable outcomes}}{\text{total outcomes}}$.
What is the multiplication rule for independent events?
What is the multiplication rule for independent events?
Tap to see back →
$P(A \text{ and } B) = P(A)P(B)$.
$P(A \text{ and } B) = P(A)P(B)$.
What is the range of probability values.
What is the range of probability values.
Tap to see back →
Between 0 and 1 inclusive.
Between 0 and 1 inclusive.