Is there a relationship between smoking and prevalence to Stenosis disease for e
ID: 3206325 • Letter: I
Question
Is there a relationship between smoking and prevalence to Stenosis disease for elderly? What is the probability that a (randomly chosen) person is not smoking? What is the probability that an elderly has Stenosis What is the probability that an elderly is not smoking and has Stenosis? What is the probability that an elderly is not smoking or has Stenosis? If the elderly is not smoking, what is the probability that he has Stenosis? Based on these data, can we assume independence between Smoking and Stenosis? An outdoor concert is scheduled on a day where the forecast indicates it might rain. if it does not rain the concert will go on and produce $30,000 in ticket sales. If it rains lightly, the concert will go on and the reduced attendance is speculated to produce just $20,000 in ticket sales. If there is heavy ram. the concert will be canceled, resulting in $0 in ticket sales. The forecast says the probability of light rain is 0.50 and the probability of heavy rain is Let X = the amount of money in ticket sales that the producer collects. Complete the probability distribution for X below. Find the expected value and the variance of X. Include your unit.Explanation / Answer
Stenosis
Smoking
Yes
No
Total
Yes
37
44
81
No
35
112
147
Total
72
156
228
( a )
P ( not smoking ) = 147 / 228 = 0.6447
Answer: 0.6447
( b )
P (stenosis) = 72 / 228 = 0.3158
Answer: 0.3158
( c )
P ( not smoking and has stenosis) = 35 / 228 = 0.1535
Answer: 0.1535
( d )
P ( not smoking or has stenosis ) = (147/228) + (72/228) – (35/228) = 0.8070
Answer: 0.8070
( e )
P ( stenosis | not smoking ) = 35 / 147 = 0.2381
Answer: 0.2381
( f )
We know that two events A and B are independent if we can show that P ( A and B ) = P ( A ) * P ( B )
Here let P ( A ) = P ( smoking )
P ( B ) = P ( stenosis )
P ( A and B ) = P ( smoking and had stenosis)
P (A ) = 81 / 228 = 0.3553
P ( B ) = 72 / 228 = 0.3158
P ( A ) * P ( B ) = 0.3553 * 0.3158 = 0.1122
P ( A and B ) = 35 / 228 = 0.1535
So we find that P ( A and B ) is not equal to P ( A ) * P ( B ) . We cannot assume independence between Smoking and Stenosis.
Stenosis
Smoking
Yes
No
Total
Yes
37
44
81
No
35
112
147
Total
72
156
228
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