Chapter 13.4, Problem 50E

To determine

To find the probability that at least one of doctors will make a correct diagnosis.

Answer to Problem 50E

  $\frac{9979}{10000}$

Explanation of Solution

Given:

The probability of diagnosis of one doctor is $\frac{93}{100}$ and the probability of second doctor diagnosis is $\frac{97}{100}$

Calculation:

P (at least $1$ doctor) $=$ P ( $1$ doctor is correct) $+$ P (both the doctors are correct)

  $=$ P (the first is correct) $\cdot$ P (the second is wrong) $+$ P (the first is wrong) $\cdot$ P (the second is correct) $+$ P (the first is correct) $\cdot$ P (the second is correct)

  $\begin{array}{l}=\frac{93}{100}\left(1-\frac{97}{100}\right)+\frac{97}{100}\left(1-\frac{93}{100}\right)+\frac{93}{100}\cdot \frac{97}{100}\\ =\frac{958}{10000}+\frac{9021}{10000}\\ =\frac{9979}{10000}\end{array}$