Question

The results of a medical test show that of 39 people selected at random who were given the​ test, 33 tested negative and 6 tested positive. Determine the odds against a person selected at random from these 39 people testing negative on the test.

Answer 1

Given Information:

Total number of people = 39

Number of people who tested negative = 33

Number of people who tested positive = 6

Required Information:

Probability of finding a person who tested negative = ?

Answer:

P( x = 1 ) = 0.000315 = 0.0315%

Explanation:

Let the probability of success is denoted by those who test negative,

p = 33/39

p = 0.85

Then the probability of failure is denoted by those who test positive,

q = 1 - p = 1 - 0.15 = 0.85

We want to find out the probability of finding a random person who test negative.

P( x = 1 ) = (p³⁹⁻¹)(1 - p)¹

P( x = 1 ) = (0.85³⁹⁻¹)(1 - 0.15)¹

P( x = 1 ) = 0.0021*0.15

P( x = 1 ) = 0.000315

Therefore, the Probability of finding a person who tested negative is 0.0315%