Year 10 Probability 2 Way Tables or Karnaugh

Year 10 Probability

2 -Way Tables or Karnaugh Maps 2 -way tables

Two-Way Tables • Two – way tables are an alternative to Venn Diagrams • They can be written with numbers or probabilities

A A’ Total B n(A B) n(A’ B) n(B) B’ n(A B’) n(A’ B’) n(B’) Total n(A) n(A’) n( ) A A’ Total B Pr(A B) Pr(A’ B) Pr(B) B’ Pr(A B’) Pr(A’ B’) Pr(B’) Total Pr(A) Pr(A’) 1

Example: In a class of 24 students there are 10 students with at least one parent who was born overseas, 7 students who are fluent in a second language and 4 who speak a second language and have at least one parent born overseas. Let B = {a parent born overseas} and let L = {fluent in a 2 nd Language} (a) Display this information as a Venn Diagram. (b) Draw a “number” two-way table B B’ Total (c) Draw a “probability” two-way table B B’ Total L 4 3 7 L’ 6 11 17 Total 10 14 24 L L’ Total

L L’ Total B B’ Total What is: (a) Pr(B) 1 (b) Pr(L) (c) Pr(B L) (d) Pr(B L)

Some college students were asked to choose which of the three subjects, English, maths or science they enjoyed most. Complete the two-table below. Girls Boys Total English Maths Sci Total 20 13 17 50 233 Completing 15 18 56 28 106 38 40

Some college students were asked to choose which of the three subjects, English, maths or science they enjoyed most. The information is displayed in the two-way table below. English Girls Boys Total Maths Sci 13 17 Probability 23 15 18 3 28 38 40 20 Total 50 56 106 What is the probability that a person selected at random: 1. Chose science as their favourite subject? 40/106 20/53 2. Chose English as their favourite subject? 38/106 19/53 3. Was a boy? 56/106 28/53 4. Was a girl who’s favourite subject was English? 20/106 10/53 5. Was a boy who’s favourite subject was maths? 15/106

Exercise 8 B Proficiency/Enrichment Understanding Fluency Problem-solving Reasoning Enrichment Foundation Standard 8, 9 b 12, 13, 14 — — Advanced — -