Favorable Outcome Probability
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ISEE Lower Level: Mathematics Achievement › Favorable Outcome Probability
The month of April has 30 days. If a date in April is chosen at random, what is the probability that the date is a two-digit number?
\(\frac{7}{10}\)
\(\frac{2}{3}\)
\(\frac{11}{15}\)
\(\frac{3}{10}\)
Explanation
The total number of outcomes is 30, since there are 30 days in April. The favorable outcomes are the two-digit dates. These are the numbers from 10 to 30. To count them, we can calculate 30 - 10 + 1 = 21. There are 21 two-digit dates in April. The probability is \(\frac{21}{30}\). This fraction simplifies by dividing the numerator and denominator by 3, resulting in \(\frac{7}{10}\).
A gumball machine contains 50 gumballs: 22 are red, 18 are blue, and the rest are green. What is the probability of getting a gumball that is not red?
\(\frac{3}{5}\)
\(\frac{14}{25}\)
\(\frac{9}{25}\)
\(\frac{11}{25}\)
Explanation
The total number of gumballs is 50. The number of gumballs that are not red is the total number of gumballs minus the number of red gumballs: 50 - 22 = 28. Alternatively, we can add the number of blue and green gumballs. Green gumballs = 50 - 22 - 18 = 10. So, non-red gumballs = 18 (blue) + 10 (green) = 28. The probability is \(\frac{28}{50}\), which simplifies to \(\frac{14}{25}\).
A vending machine contains 12 bags of pretzels, 15 bags of potato chips, and 13 bags of corn chips. If a snack is randomly dispensed, what is the probability that it is either potato chips or corn chips?
\(\frac{13}{40}\)
\(\frac{3}{8}\)
\(\frac{7}{10}\)
\(\frac{3}{10}\)
Explanation
First, find the total number of snacks in the machine: 12 + 15 + 13 = 40. This is the total number of outcomes. The favorable outcomes are potato chips or corn chips. The number of these is 15 + 13 = 28. The probability is the ratio of favorable outcomes to the total, which is \(\frac{28}{40}\). Dividing both numerator and denominator by 4 simplifies the fraction to \(\frac{7}{10}\).
The numbers from 10 to 30, inclusive, are written on separate slips of paper and put into a jar. If one slip is drawn at random, what is the probability the number is divisible by 5?
\(\frac{4}{21}\)
\(\frac{1}{4}\)
\(\frac{5}{21}\)
\(\frac{1}{6}\)
Explanation
First, determine the total number of slips. The numbers are from 10 to 30, inclusive. The count is 30 - 10 + 1 = 21 slips. This is the total number of outcomes. Next, find the favorable outcomes: numbers divisible by 5. These are 10, 15, 20, 25, and 30. There are 5 such numbers. The probability is \(\frac{5}{21}\).
A bag contains 8 red marbles, 5 blue marbles, and 7 green marbles. If one marble is drawn at random from the bag, what is the probability that the marble is not blue?
\(\frac{1}{4}\)
\(\frac{4}{5}\)
\(\frac{3}{4}\)
\(\frac{1}{3}\)
Explanation
First, find the total number of marbles: 8 (red) + 5 (blue) + 7 (green) = 20 marbles. The number of favorable outcomes is the number of marbles that are not blue, which is 8 (red) + 7 (green) = 15 marbles. The probability is the ratio of favorable outcomes to the total number of outcomes, which is \(\frac{15}{20}\). Simplified, this fraction is \(\frac{3}{4}\).
A standard six-sided die is rolled one time. What is the probability that the number rolled is a prime number?
\(\frac{5}{6}\)
\(\frac{1}{3}\)
\(\frac{1}{2}\)
\(\frac{2}{3}\)
Explanation
A standard six-sided die has faces numbered 1, 2, 3, 4, 5, 6. The total number of outcomes is 6. The prime numbers between 1 and 6 are 2, 3, and 5. Note that 1 is not a prime number. There are 3 favorable outcomes. The probability is the number of favorable outcomes divided by the total number of outcomes, which is \(\frac{3}{6}\), or \(\frac{1}{2}\).
A box of 24 crayons contains 6 red crayons and 8 blue crayons. The rest of the crayons are yellow. If a crayon is chosen at random, what is the probability that it is yellow?
\(\frac{5}{12}\)
\(\frac{1}{4}\)
\(\frac{7}{12}\)
\(\frac{1}{3}\)
Explanation
First, find the number of yellow crayons. There are 24 crayons in total, with 6 red and 8 blue. The number of yellow crayons is 24 - (6 + 8) = 24 - 14 = 10. The total number of outcomes is 24. The number of favorable outcomes (picking a yellow crayon) is 10. The probability is \(\frac{10}{24}\), which simplifies to \(\frac{5}{12}\).
A spinner is divided into 12 equal sections, which are numbered from 1 to 12. What is the probability of the spinner landing on a number that is a multiple of 3?
\(\frac{1}{12}\)
\(\frac{1}{4}\)
\(\frac{1}{3}\)
\(\frac{1}{2}\)
Explanation
The total number of possible outcomes is 12, as there are 12 sections. The favorable outcomes are the multiples of 3 between 1 and 12, which are 3, 6, 9, and 12. There are 4 favorable outcomes. The probability is the ratio of favorable outcomes to total outcomes, which is \(\frac{4}{12}\). This fraction simplifies to \(\frac{1}{3}\).
In a classroom of 30 students, 18 are girls. If the teacher randomly calls on one student to answer a question, what is the probability that the student is a boy?
\(\frac{3}{5}\)
\(\frac{2}{5}\)
\(\frac{2}{3}\)
\(\frac{1}{2}\)
Explanation
First, determine the number of boys in the class. If there are 30 students in total and 18 are girls, then the number of boys is 30 - 18 = 12. The total number of possible outcomes is 30. The number of favorable outcomes (selecting a boy) is 12. The probability is \(\frac{12}{30}\). This fraction simplifies by dividing both the numerator and denominator by 6, which gives \(\frac{2}{5}\).
There are seven days in a week. If a day of the week is chosen at random, what is the probability that its name contains the letter 'd'?
\(\frac{4}{7}\)
\(\frac{6}{7}\)
\(\frac{5}{7}\)
\(\frac{2}{7}\)
Explanation
This is a probability question asking you to find the likelihood of a specific outcome when selecting randomly from a group. Probability equals the number of favorable outcomes divided by the total number of possible outcomes.
Let's identify which days of the week contain the letter 'd': Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday. Checking each name: Monday (yes), Tuesday (yes), Wednesday (yes), Thursday (yes), Friday (yes), Saturday (yes), Sunday (yes). Wait - let me check more carefully. The days containing 'd' are: Monday, Tuesday, Wednesday, Thursday, and Saturday. That's 5 days out of 7 total days, so the probability is $$\frac{5}{7}$$.
Looking at the wrong answers: Choice A ($$\frac{2}{7}$$) suggests you only counted two days with 'd' - perhaps you only noticed obvious ones like Wednesday and Thursday. Choice B ($$\frac{4}{7}$$) means you missed one day, likely Saturday since the 'd' appears in the middle of "Saturday." Choice C ($$\frac{6}{7}$$) indicates you incorrectly included one extra day - possibly thinking Sunday contains 'd' when it contains 'n'.
The correct answer is D: $$\frac{5}{7}$$.
Strategy tip: For probability questions involving letters in words, write out each option and carefully examine the spelling. Don't rely on quick mental scanning - the letter you're looking for might appear in unexpected positions within the words. Always double-check your count of favorable outcomes before calculating the fraction.