Question

A local grocery store tested spinach samples for E coli bacteria using two different tests. The first test has a 94% probability of giving accurate results, while the second test is accurate 89% of the time. A sample that contains E coli bacteria is tested.
The probability that both tests detect the bacteria is _%

Answer 1

Answer:  Probability that both tests detect the bacteria is 83.66%.

Step-by-step explanation:

Since we have given that

Probability of  the first test giving accurate results = 84%

Probability of the second test is accurate = 89%

Probability of both tests detect the bacteria is given by

$\frac{94}{100}\times \frac{89}{100}\\\\=0.94\times 0.89\\\\=0.8366\\\\=83.66\%$

Hence, Probability that both tests detect the bacteria is 83.66%.

Answer 2

The results of the tests are independent. Therefore the probability that both tests detect the bacteria is:
$0.94\times0.89=0.8366$
As a percentage we could say 83.66%