General Probability Rules
A recent survey of 500 randomly selected college students indicates that 210 drink coffee while studying, 185 snack while studying, and 95 do both (not necessarily at the same time) while studying. Define the events C = drinks coffee while studying and S = snacks while studying.
Find P(C and S).
0.19
As of March 1, 2026, 150 campus flu cases were reported at a university. Students under 20 made up 40% of cases (25% hospitalized), ages 20–25 accounted for 45% (15% hospitalized), adults 26 and older made up 12% (30% hospitalized), and age was unknown for 3% (40% hospitalized).
One flu case is selected at random. What is the probability that the case was an individual 20–25 and they were not hospitalized?
0.3825
Advanced Placement (AP) tests are assigned a numerical score from 1 to 5. The College Board reports the distribution of scores on the AP Chemistry exam as follows:
Find P(X ≥ 4).
0.18
Suppose a continuous random variable X is defined on the interval 0 ≤ X ≤ 1.3 with a density function f(x) shaped as shown in the graph.
What is the probability that X is less than or equal to 0.7 (P(X ≤ 0.7))?
0.70
The daily recovery time for a certain minor outpatient surgery is approximately normally distributed, N(5.5, 1.2), where mean mu = 5.5 days and standard deviation = 1.2 days.
Find the z-score for a recovery time that lasts $7.5$ days.
1.67
A recent survey of 500 randomly selected college students indicates that 210 drink coffee while studying, 185 snack while studying, and 95 do both (not necessarily at the same time) while studying. Define the events C = drinks coffee while studying and S = snacks while studying.
Find P(C or S).
0.60
As of March 1, 2026, 150 campus flu cases were reported at a university. Students under 20 made up 40% of cases (25% hospitalized), ages 20–25 accounted for 45% (15% hospitalized), adults 26 and older made up 12% (30% hospitalized), and age was unknown for 3% (40% hospitalized).
One flu case is selected at random. What is the probability that the case resulted in hospitalization?
0.2155
Advanced Placement (AP) tests are assigned a numerical score from 1 to 5. The College Board reports the distribution of scores on the AP Chemistry exam as follows:
Calculate E[X], the long-range average score.
2.35
Suppose a continuous random variable X is defined on the interval 0 ≤ X ≤ 1.3 with a density function f(x) shaped as shown in the graph.
What is the probability that X is greater than 0.7 (P(X > 0.7))?
0.30
The daily recovery time for a certain minor outpatient surgery is approximately normally distributed, N(5.5, 1.2), where mean mu = 5.5 days and standard deviation = 1.2 days.
According to the Empirical Rule, what is the approximate probability that a randomly selected individual has a recovery time that is 3.1 days or fewer?
0.025
A recent survey of 500 randomly selected college students indicates that 210 drink coffee while studying, 185 snack while studying, and 95 do both (not necessarily at the same time) while studying. Define the events C = drinks coffee while studying and S = snacks while studying.
Find P(Cc).
0.58
As of March 1, 2026, 150 campus flu cases were reported at a university. Students under 20 made up 40% of cases (25% hospitalized), ages 20–25 accounted for 45% (15% hospitalized), adults 26 and older made up 12% (30% hospitalized), and age was unknown for 3% (40% hospitalized).
One flu case that results in hospitalization is selected randomly. What is the probability that the individual was under 20?
0.4640
Advanced Placement (AP) tests are assigned a numerical score from 1 to 5. The College Board reports the distribution of scores on the AP Chemistry exam as follows:
Find the standard deviation of X.
1.16
Suppose a continuous random variable X is defined on the interval 0 ≤ X ≤ 1.3 with a density function f(x) shaped as shown in the graph.
What is the probability that X is between 0.4 and 1.3 (P(0.4 ≤ X ≤ 1.3))?
0.60
The daily recovery time for a certain minor outpatient surgery is approximately normally distributed, N(5.5, 1.2), where mean mu = 5.5 days and standard deviation = 1.2 days.
According to the Empirical Rule, what is the approximate probability that a randomly selected individual has a recovery time that is between 4.3 and 6.7 days?
0.68