A group of 30 people are going on a snowboarding trip to Mammoth. Twenty-five of
ID: 3170216 • Letter: A
Question
A group of 30 people are going on a snowboarding trip to Mammoth. Twenty-five of them plan to snowboard at the beginner level-12 who ride switch and 13 ride regular. The other 5 are going to snowboard the advanced black diamond runs-12 who ride switch and 13 who ride regular. Let B be the event that you are going to ride the beginner runs. Let R be the event that you ride regular on your snowboard. a. Construct a contingency table for the problem. Fill in all cells with the appropriate probabilities Construct a Venn diagram for the problem. Fill in the four areas with the appropriate probabilities What is the probability that a person is neither a beginner nor riding regular? d. What is the probability that a person is either a beginner or has a rides regular? e. Given that a snowboarder is in the beginner run, what is the probability they are riding switch? f. Are the events "Beginner Run" and "Riding Regular" independent?Explanation / Answer
b. Venn Diagram Probabilities will be as follows(Unable to upload picture)
c. The probability that a person is neither a beginner nor riding regular refers to the probabilty that person is Riding switch and riding advance which is 2/30 i.e. 0.07
d. This probability is complete opposite of probability mentioned in 'c' and as we know sum of the probability is always one, we can directly deduct that probability obtained in 'c' from 1 to get our desired probability i.e. 1-0.07 = 0.93
e. This is the question of conditional probability where one event has already occured and we need to find the probability of other event. Hence we will write it as P(Rc/B) = P(Rc n B ) / P(B) = (12/30) / (25/30) = 0.48
f. Yes Beginner Run(B) and Ridng Regular(R) are independet events as they do not affect occurence of events or we can say outcome of Beginner run has no effect on outcome of Riding regular. In probability independent events are represented as P(A n B) = P(A).P(B)
a. Beginner Run(B) Advance Run(Bc) Total Ride Regular R 0.43 0.10 0.53 Ride Switch(Rc) 0.40 0.07 0.47 Total 0.83 0.17 1Related Questions
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