Question

A doctor is concerned about the relationship between blood pressure and irregular heartbeats. Among her patients, she classifies blood pressures as high, normal, or low, and heartbeats as regular or irregular and finds that (a) 15 % have high blood pressure; (b) 9 % have low blood pressure; (c) 20 % have irregular heartbeats; (d) of those with an irregular heartbeat, 36 % have high blood pressure; and (e) of those with normal blood pressure, 9 % have an irregular heartbeat. Suppose a patient is chosen at random.

What is the probability the patient has a irregular heartbeat and normal blood pressure?

Answer 1

The probability that a randomly chosen patient has an irregular heartbeat and normal blood pressure is 6.84%, calculated by multiplying the percentage of patients with normal blood pressure (76%) by the percentage of those patients who have an irregular heartbeat (9%).

Step-by-step explanation:

The question asks for the probability that a randomly chosen patient has an irregular heartbeat and normal blood pressure. According to the provided information, we already know that:

• 20% of patients have irregular heartbeats.
• 36% of those with an irregular heartbeat have high blood pressure, hence 64% have normal or low blood pressure.
• Of those with normal blood pressure, 9% have an irregular heartbeat.
• Since 15% have high blood pressure and 9% have low blood pressure, the remaining 76% (100% - 15% - 9%) have normal blood pressure.

To find the probability of a patient having both an irregular heartbeat and normal blood pressure, we'll multiply the percentage of patients with normal blood pressure by the percentage of those who also have an irregular heartbeat:

P(Irregular heartbeat and Normal blood pressure) = P(Normal blood pressure) * P(Irregular heartbeat | Normal blood pressure)

So we calculate:

P(Irregular heartbeat and Normal blood pressure) = 0.76 * 0.09

After performing the multiplication:

P(Irregular heartbeat and Normal blood pressure) = 0.0684 or 6.84%

The probability that a randomly chosen patient has an irregular heartbeat and normal blood pressure is 6.84%.