Question

Health Rights Hotline published the results of a survey of 2,400 people in Northern California in which consumers were asked to share their complaints about managed care. The number one complaint was denial of care, with 17% of the participating consumers selecting it. Several other complaints were noted, including inappropriate care (14%), customer service (14%), payment disputes (11%), specialty care (10%), delays in getting care (8%), and prescription drugs (7%). These complaint categories are mutually exclusive. Assume that the results of this survey can be inferred to all managed care consumers. If a managed care consumer is randomly selected, determine the following probabilities:

1. The consumer complains about payment disputes or specialty care.
2. The consumer complains about prescription drugs and customer service.
3. The consumer complains about inappropriate care given that the consumer complains about specialty care.
4. The consumer does not complain about delays in getting care nor does the consumer complain about payment disputes.

Answer 1

The number one complaint was denial of care, with 17% of the participating consumers selecting it.

Several other complaints were noted, including
denial of care, with 17%
inappropriate care (14%),
customer service (14%),
payment disputes (11%),
specialty care (10%),
delays in getting care (8%),
prescription drugs (7%)

The consumer complains about payment disputes or specialty care.

P(payment disputes or specialty care) = P(payment dispute)+P(specialty care)= 0.11+0.10 = 0.21

since they are mutually exclusive we can simply add the probability.

The consumer complains about prescription drugs and customer service.
P(prescription drugs and customer service)=0

since they are mutually exclusive we willnot have any thing in comman.

The consumer complains about inappropriate care given that the consumer complains about specialty care.

P(inappropriate care |specialty care) = P(inappropriate care) = 0.14
Since they are mutually exclusive the conditional probability has not impact.

The consumer does not complain about delays in getting care nor does the consumer complain about payment disputes.

P(no delays in getting care or no payment disputes) = 1- P( delays in getting care or payment disputes) = 1 - (0.08 + 0.11) = 1-0.19 = 0.81