Two sets of numbers, $A$A and $B$B, are such that set $A$A contains the even numbers from $1$1 to $20$20, inclusive, and set $B$B contains the factors of $48$48 from $1$1 to $20$20, inclusive.

Easy

6min

At a university there are $816$816 students studying first year engineering, $497$497 of whom are female (set $F$F). $237$237 of these women are studying Civil Engineering, and there are $348$348 students studying Civil Engineering altogether (set $C$C).

Medium

8min

At an Italian restaurant, $Alessandra$ orders an entree, main and dessert. She has $2$2 entrees, $3$3 mains and $2$2 desserts to choose from.

Entrees: calamari, soup

Mains: spaghetti, lasagna, risotto

Dessert: gelato, tiramisu

Medium

5min

Outcomes

NC.M2.S-CP.3

Develop and understand independence and conditional probability.

NC.M2.S-CP.3a

Use a 2-way table to develop understanding of the conditional probability of a given b (written p(a|b)) as the likelihood that a will occur given that b has occurred. That is, p(a|b) is the fraction of event b’s outcomes that also belong to event a.

NC.M2.S-CP.3b

Understand that event a is independent from event b if the probability of event a does not change in response to the occurrence of event b. That is p(a|b)=p(a).

NC.M2.S-CP.4

Represent data on two categorical variables by constructing a two-way frequency table of data. Interpret the two-way table as a sample space to calculate conditional, joint and marginal probabilities. Use the table to decide if events are independent.

NC.M2.S-CP.5

Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations.

NC.M2.S-CP.6

Find the conditional probability of a given b as the fraction of b’s outcomes that also belong to a, and interpret the answer in context.

11.07 Conditional probability

Interactive practice questions