ISEE Lower Level Mathematics Achievement Flashcards: Real World Probability

What this deck covers

This deck focuses on Real World Probability, giving you a quick way to review the definitions, rules, and examples that matter most for ISEE Lower Level Mathematics Achievement.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Flashcard 1: What is $P(A)$ if $P(A^c)=0.27$?

Answer: $0.73$. Apply the complement rule: subtract $P(A^c)$ from 1 to find $P(A)$.

Flashcard 2: What is the probability that a randomly chosen month has $31$ days?

Answer: $\frac{7}{12}$. Seven months (Jan, Mar, May, Jul, Aug, Oct, Dec) have 31 days out of 12.

Flashcard 3: What is the probability of drawing a red card from a standard $52$-card deck?

Answer: $\frac{1}{2}$. Standard deck has 26 red cards out of 52 total cards.

Flashcard 4: What is the probability of rolling an even number on a fair die?

Answer: $\frac{1}{2}$. Three even numbers (2,4,6) out of six possible outcomes on a fair die.

Flashcard 5: What is the probability of rolling a $2$ or $5$ on one fair die?

Answer: $\frac{1}{3}$. Two favorable outcomes (2 or 5) out of six, mutually exclusive.

Flashcard 6: What is the probability of flipping two heads in $2$ fair coin flips?

Answer: $\frac{1}{4}$. Independent flips each with probability $\frac{1}{2}$, so multiply for both heads.

Flashcard 7: What is the probability of drawing a heart from a standard $52$-card deck?

Answer: $\frac{1}{4}$. Thirteen hearts out of 52 cards in a standard deck.

Flashcard 8: What is the probability of choosing a green marble from $3$ blue and $5$ green marbles?

Answer: $\frac{5}{8}$. Five green marbles out of eight total marbles.

Flashcard 9: What is the formula for probability when outcomes are equally likely?

Answer: $P(A)=\frac{\text{favorable outcomes}}{\text{total outcomes}}$. When all outcomes are equally likely, probability is the ratio of favorable to total outcomes.

Flashcard 10: What is the probability of rolling a $6$ on a fair six-sided die?

Answer: $\frac{1}{6}$. One favorable outcome out of six equally likely die faces.

Flashcard 11: What inequality must any probability $P(A)$ satisfy?

Answer: $0\le P(A)\le 1$. Probabilities range from zero for impossibility to one for certainty, inclusive.

Flashcard 12: What is the probability of choosing a blue marble from $3$ blue and $5$ green marbles?

Answer: $\frac{3}{8}$. Three blue marbles out of eight total marbles.

Flashcard 13: What is the probability of drawing an ace from a standard $52$-card deck?

Answer: $\frac{1}{13}$. Four aces in a 52-card deck simplify to this fraction.

Flashcard 14: What is the probability of choosing a vowel from the letters in the word $\text{MATH}$?

Answer: $\frac{1}{4}$. One vowel (A) among the four letters M, A, T, H.

Flashcard 15: What is the complement rule for an event $A$?

Answer: $P(A^c)=1-P(A)$. The complement covers all outcomes not in $A$, so its probability is one minus $P(A)$.

Flashcard 16: What is the probability of an event that is certain?

Answer: $1$. A certain event includes all possible outcomes, yielding probability one.

Flashcard 17: What is the probability of flipping at least one head in $2$ fair coin flips?

Answer: $\frac{3}{4}$. Out of four possible outcomes in two flips, three include at least one head.

Flashcard 18: What is the probability that a random integer from $1$ to $10$ is a multiple of $3$?

Answer: $\frac{3}{10}$. Three multiples of 3 (3,6,9) from integers 1 to 10.

Flashcard 19: What is the probability of an event that is impossible?

Answer: $0$. An impossible event has no favorable outcomes, resulting in zero probability.

Flashcard 20: What is $P(A\text{ or }B)$ if $A$ and $B$ are mutually exclusive?

Answer: $P(A\text{ or }B)=P(A)+P(B)$. Mutually exclusive events have no overlap, so add their probabilities for the union.

Flashcard 21: What is the probability of not rolling a $6$ on one fair die?

Answer: $\frac{5}{6}$. Complement of rolling a 6, which has probability $\frac{1}{6}$, subtracted from 1.

Flashcard 22: What is the probability that a randomly chosen day of the week is a weekend day?

Answer: $\frac{2}{7}$. Two weekend days (Saturday, Sunday) out of seven days in a week.

Flashcard 23: What is $P(A\text{ and }B)$ if $A$ and $B$ are independent?

Answer: $P(A\text{ and }B)=P(A)\cdot P(B)$. Independent events' occurrences don't affect each other, so multiply probabilities for intersection.

Flashcard 24: What is the probability that a random integer from $1$ to $20$ is prime?

Answer: $\frac{8}{20}$. Eight primes (2,3,5,7,11,13,17,19) from integers 1 to 20.