IMAT Mathematics: Part 4

An interactive quiz on Probability and Statistics.

Fundamental Concepts Review

Probability: The likelihood of an event is $\frac{\text{Favorable Outcomes}}{\text{Total Outcomes}}$. For complex counting, use combinations ($_{n}C_{r}$) when order doesn't matter.

Conditional Probability: The probability of event A given B is $P(A|B) = \frac{P(A \cap B)}{P(B)}$. This is key for problems where information is revealed sequentially.

Statistical Measures: Be fluent in calculating the mean (average), median (middle value), and mode (most frequent value). Variance ($\sigma^2$) measures the spread, calculated as the average of the squared distances from the mean.

Problem 14: Conditional Probability

Hard
ProbabilityConditional ProbabilityBayes' Theorem

Bag A contains 3 red and 5 blue balls. Bag B contains 5 red and 3 blue balls. A bag is chosen at random, and a ball is drawn from it. If the ball is red, what is the probability it came from Bag A?

A

$\frac{1}{2}$

B

$\frac{3}{8}$

C

$\frac{9}{25}$

D

$\frac{1}{4}$