ISEE Lower Level Mathematics Achievement Flashcards: Favorable Outcome Probability

What this deck covers

This deck focuses on Favorable Outcome 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 the probability of choosing a blue marble from $5$ red and $3$ blue marbles?

Answer: $\frac{3}{8}$. With 3 blue marbles out of a total of 8, the ratio determines the probability of selecting blue.

Flashcard 2: What is the probability of choosing a prime number from the integers $1$ through $10$?

Answer: $\frac{2}{5}$. Prime numbers between 1 and 10 (2, 3, 5, 7) are four out of ten integers.

Flashcard 3: What is the probability of getting exactly one head in two fair coin flips?

Answer: $\frac{1}{2}$. The sample space has four outcomes (HH, HT, TH, TT), with exactly one head occurring in two of them (HT, TH).

Flashcard 4: What is the probability of choosing a consonant from the letters in the word MATH?

Answer: $\frac{3}{4}$. The word MATH has four letters, with three consonants (M, T, H).

Flashcard 5: What is the probability of choosing a multiple of $3$ from the integers $1$ through $9$?

Answer: $\frac{1}{3}$. From 1 to 9, the multiples of 3 (3, 6, 9) are three out of nine integers.

Flashcard 6: What is the probability of choosing a heart from a standard $52$-card deck?

Answer: $\frac{1}{4}$. A standard deck has 13 hearts out of 52 cards, assuming equal likelihood.

Flashcard 7: What is the probability of choosing a vowel from the letters in the word MATH?

Answer: $\frac{1}{4}$. The word MATH has four letters, with one vowel (A) among them.

Flashcard 8: What is the probability of choosing a number less than $5$ from the integers $1$ through $10$?

Answer: $\frac{2}{5}$. Numbers less than 5 (1, 2, 3, 4) are four out of ten integers from 1 to 10.

Flashcard 9: What is the probability of choosing a face card from a standard $52$-card deck?

Answer: $\frac{3}{13}$. There are 12 face cards (J, Q, K in 4 suits) out of 52 cards in a standard deck.

Flashcard 10: What is the probability of rolling a number greater than $4$ on a fair $6$-sided number cube?

Answer: $\frac{1}{3}$. Numbers greater than 4 (5, 6) are two out of six possible outcomes on a fair cube.

Flashcard 11: What is the probability of rolling an even number on a fair $6$-sided number cube?

Answer: $\frac{1}{2}$. Even numbers (2, 4, 6) are three out of six possible outcomes on a fair cube.

Flashcard 12: What is the probability of choosing a black card from a standard $52$-card deck?

Answer: $\frac{1}{2}$. Half of the 52 cards in a standard deck are black (spades and clubs).

Flashcard 13: What is the probability of choosing a number greater than $3$ on a fair spinner labeled $1$ to $8$?

Answer: $\frac{5}{8}$. Numbers greater than 3 (4 through 8) are five out of eight possible outcomes on the spinner.

Flashcard 14: What is the probability of choosing a month with $31$ days from the $12$ months of the year?

Answer: $\frac{7}{12}$. Seven months (January, March, May, July, August, October, December) have 31 days out of 12.

Flashcard 15: What is the probability of choosing a weekend day from the $7$ days of the week?

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

Flashcard 16: What is the probability of an event that has $0$ favorable outcomes out of $n$ total outcomes?

Answer: $0$. An event with no favorable outcomes is impossible, resulting in zero probability regardless of the total outcomes.

Flashcard 17: What is the probability of choosing an ace from a standard $52$-card deck?

Answer: $\frac{1}{13}$. A standard deck has 4 aces out of 52 cards.

Flashcard 18: What is the probability of choosing a factor of $12$ from the integers $1$ through $12$?

Answer: $\frac{1}{2}$. Factors of 12 (1, 2, 3, 4, 6, 12) are six out of twelve integers from 1 to 12.

Flashcard 19: What is the probability of getting at least one head in two fair coin flips?

Answer: $\frac{3}{4}$. Three out of four outcomes in two coin flips include at least one head (HH, HT, TH).

Flashcard 20: What is the formula for probability using favorable outcomes and total outcomes?

Answer: $P(\text{event})=\frac{\text{favorable outcomes}}{\text{total outcomes}}$. This formula defines the probability of an event as the ratio of favorable outcomes to total possible outcomes in a sample space assuming equal likelihood.

Flashcard 21: What is the probability of rolling a $4$ on a fair $6$-sided number cube?

Answer: $\frac{1}{6}$. A fair 6-sided cube has one favorable outcome (4) out of six equally likely outcomes.

Flashcard 22: What is the probability of an event that has $n$ favorable outcomes out of $n$ total outcomes?

Answer: $1$. When all outcomes are favorable, the event is certain, yielding a probability of one.

Flashcard 23: What is the probability of flipping heads on a fair coin?

Answer: $\frac{1}{2}$. A fair coin has two equally likely outcomes, with heads being one of them.

Flashcard 24: What is the probability of choosing a red marble from $5$ red and $3$ blue marbles?

Answer: $\frac{5}{8}$. With 5 red marbles out of a total of 8, the ratio gives the probability of selecting red.

Flashcard 25: What is the probability of getting two heads in two fair coin flips?

Answer: $\frac{1}{4}$. Out of four possible outcomes in two coin flips, only one (HH) results in two heads.