13) A political discussion group consisting of 6 Democrats, 3 Republicans, and7

Question

13) A political discussion group consisting of 6 Democrats, 3 Republicans, and7 Independents. Two group members are randomly selected to attend a political convention. an Independent and then a Democrat. Find the probability of selecting 14) A study was recently done that emphasized the problem we all face with drinking and driving. Four hundred accidents that occurred on a Saturday night were analyzed. The numbers are shown below Number of Vehicles Involved Did Alcohol Play a Role?1 or 2 more Totals 21 35 230 56 400 Yes55 94 No25 170 Totals80 264 170 a) Given that an accident involved multiple vehicles, what is the probability that it involved alcohol? b) If alcohol was not involved, what is the probability that it involved 3 or more cars? 15) A lab orders a shipment of 100 rats a week, 52 weeks a year, from a rat supplier for experiments that the lab conducts. Prices for each weekly shipment of rats follow the distribution below: Price $10.00 $12.50 $15.00 0.3 Probability0.2 How much should the lab budget for next year's rat orders assuming this distribution does not change. (Hint: find the expected price.) 0.5

Explanation / Answer

13)

Total number of members: 6+3+7 = 16

Out of 16, 7 are independent. So the probability of selecting a indepedent first is

P(independent first) = 7/16

After than out of rwmaing 15 peoples, 6 are democrat so

P(second democrat | independent first) = 6/15

Therefore the required probability is

P(second democrat and independent first) = P(second democrat | independent first)P(independent first) =(6/15) * (7/16) = 0.175

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