A medical team sent surveys to randomly selected households to determine the various health problems. The result of the survey is shown below.

health problems, number of patients

obesity 32

diabetes 54

heart problems 78

eye problems 112

dental problems 96

Note: The survey result for each health problem is mutually exclusive.

Based on the survey, what is the probability that a person chosen at random is a diabetic patient or an eye patient?

(SHOW WORK)

Answer:0.45

Step-by-step explanation: For mutually exclusive events, the probability of randomly choosing a Diabetic or Eye patient (DP or EP) is equivalent to the probability of choosing DP plus the probability of choosing EP.

Probability of choosing DP = Number of DP/Total number of patients

= 54 / (32+54+78+112+96)

=54/372

=9/62

Probability of choosing EP = Number of EP/Total number of patients

= 112 / (32+54+78+112+96)

=112/372

=28/93

Probability of choosing DP or EP = (9/62) + (28/93)

= 18/186

= 0.45