Suppose we did collect data by asking professors how old they were and measuring
ID: 3131115 • Letter: S
Question
Suppose we did collect data by asking professors how old they were and measuring their blood pressure. The table below reflects the data collected based on these two variables:
Low Blood Pressure
High Blood Pressure
Total
50 and Under
64
51
115
Over 50
31
73
104
Total
95
124
219
Let us use the following notation for events: U = 50 and under, O = over 50, L = low blood pressure and H = high blood pressure.
1. Compute P(L), P(L|U) and P(L|O).
2. Are the events L = low blood pressure and U = 50 and under independent? Why or why not?
3. Compute P(L and U) and P(L and O).
4. Compute P(H) and P(H|U).
5. Are the events H = high blood pressure and O = over 50 independent? Why or why not?
6. Compute P(L or U).
Low Blood Pressure
High Blood Pressure
Total
50 and Under
64
51
115
Over 50
31
73
104
Total
95
124
219
Explanation / Answer
Answer to question# 1)
P(L) = total number of Low Blood Pressure people / total number of people
P(L) = 95 /219
.
P(L | U) = P(L and U ) / P(U) ...formula of conditional probability
P(L and U ) = probability of people under 50 and have low BP = 64/219
P(U) = Probability of people under 50 = 115/219
.
P(L | U) = (64 /219) / (115 /219)
P(L | U) = 64 /115
.
P(L | O) = P(L and O) / P(O)
P(L and O) = 31 /219
P(O) = 104 /219
P( L | O) = (31 /219 ) / (104 /115)
P(L | O) = 31 /104