Cyclists over the age of 13 in MA do not have to wear helmets. Suppose you have

Question

Cyclists over the age of 13 in MA do not have to wear helmets. Suppose you have data collected based on whether or not an adult cyclist is wearing a helmet and whether or not automobiles pass close or leave additional space for the cyclist. The data is summarized in the table. Treat the counts collected as population information to answer the following questions. What is the probability a randomly selected cyclist is wearing a helmet? What is the probability a randomly selected cyclist was passed close? What is the probability a randomly selected cyclist was wearing a helmet and he or she was passed close. What is the probability a randomly selected cyclist was wearing a helmet or he or she was passed close What is the probability a randomly selected cyclist was not wearing a helmet given that he or she was passed close? Are pass status and wearing a helmet independent? Explain using a probability calculation. Are pass status and wearing a helmet mutually exclusive Explai

Explanation / Answer

a. P( randomly selecred cyclist is wearing a helmet) = 105/180

b. P( Randomly selected cyclist was passed close) = 84/180

c. P( was wearing a helmet and passed close) = 49/180

d. P( randomly selected cyclist was wearing a helmet or he or she was passed close) = 105+84-49 / 180 = 140/180

e.P( given she was passed close, she wasn't wearing helmet) = 35/75

f.

Yes.They are. P(A)*P(B) = P(A intersect B)

Let A be event of Pass close and B be event of No helmet.

So, Is 84/180 * 75/180 = 35/180 ? Yes. Hence, independent.

Try the next, Is 105/180 *96/180 = 56/180 . Yes. Hence indepedent.

g.

No they aren't. IF pass status and wearning helmet was Mutually exclusive then there would have been no overlap.

h.

P( 2 randomly selected cyclists would both not be wearing helmets) = 75C2/180C2

=2775/16110

=.1722

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