OPMT 1130 Myra Andrews, Judy Li Business Statistics Winter 2018

Page 1 of 10 Lecture 5: 2 × 2 Probability Tables:Put one mutually exclusiveevent and its complement along the top. Put the other mutually exclusiveevent and its complement along the left side. Inside the table put the “AND”probabilities. AATotal BBandAPBandAPBPBBandAPBandAPBPTotal APAP1 1.The BC Lottery Corp. is deciding whether or not they should allow cigarette smoking in casinos. Before making their decision they want to determine if smokers are more likely to gamble in casinos than non-smokers. They randomly select 400 adults and ask them if they gamble in a casino on a regular basis (i.e. at least once per week) and whether they smoke. 80 adults smoke •60 adults gamble in a casino at least once a week 28 adults both gamble (in a casino at least once a week) and smoke Set up a 2 × 2 table of the frequencies and answer the following questions: Smoker Non-Smoker Total Gamble Don’t GambleTotal (a)What percentage of adultsboth gamble on a regular basis and smoke? (b)What percentage of adultseithergamble or smoke? (c)What percentage of adultsneither gamble nor smoke? (d)What percentage of adults either smoke or gamble but notboth? (e)What percentage of smokersgamble in a casino on a regular basis? (f)What percentage of non-smokersgamble in a casino on a regular basis? (g)What percentage of adultsgamble in a casino on a regular basis? (h)Among those who gamble, what percentage of them also smoke? (i)If an adult smokes, what is the probability that they do notgamble? (j)What percentage of adultsare non-smokers who gamble? (k)Are gambling and smoking independent events? Prove using probability. You must use wordsor defined symbolsin your proof. Sol:

(j) 8%

OPMT 1130 Myra Andrews, Judy Li Business Statistics Winter 2018

Page 2 of 10 2.Christine has always struggled in math. Based on her performance prior to the final exam in Business Math, there is a 60% chance that she will fail the course if she does notget a tutor. With a tutor, her probability of failing decreases to 20%. There is only a 55% chance she will find a tutor with such short notice. (a)The probability that Christine fails the course must be between what two values? (b)What is the probability that Christine fails the course? (Set up a 2×2 probability table). Total Total