Favorable Outcome Probability - ISEE Lower Level: Mathematics Achievement

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

$P(\text{event})=\frac{\text{favorable outcomes}}{\text{total outcomes}}$. 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.

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