Homework One SolutionsDue August 30, 20131. Event A occurs with probability 0.7 and event B occurs with probability 0.4.(a) What is the largest union A and B can have?

(b) What is the smallest union A and B can have?

(c) What is the largest intersection A and B can have?

(d) What is the smallest intersection A and B can have?

2. Of the faculty at Purdue, 65% drink coffee, 70% do not drink tea, and 90% either don’tdrink coffee or don’t drink tea.(a) Draw a Venn Diagram of the faculty at Purdue describing their drink preferences.

T

(b) What is the probability a randomly chosen faculty member at Purdue drinks onlycoffee?

(c) What is the probability a randomly chosen faculty member at Purdue does not drinkcoffee and does not drink tea?

(d) What is the probability a randomly chosen faculty member at Purdue drinks coffeegiven they do not drink tea?

(e) What is the probability a randomly chosen faculty member at Purdue drinks bothcoffee and tea given they drink coffee or tea?

3. You randomly choose a letter from{A, B, C, D, E}and a friend randomly chooses a letterfrom{a, b, c, d, e}to create a pair of 2 letters with 1 capital letter and 1 lower case letter.(a) What is the sample space of letter pairs possible?

(b) What is the probability a pair of letters has at least 1 vowel?

(c) What is the probability a pair of letters has exactly 1 vowel?

(d) What is the probability the two letters are the same?

4. Each parent has 3 alleles,{a, b, o}. Each parent gives one allele to the offspring, and thecombination determines the blood type of the offspring,{A, B, AB, O}.Ordering of thealleles does not matter, so the allele pairsabandbaact in the same way and determine thesame blood type. The following table summarizes the allele pairs and blood types (withoutallele pairing repetition):(a) What is the probability the child has blood typeA?