The director of student health decides to test every student on campus for tuberculosis. If there are 3000 students out of which only 50 have tuberculosis and the probability of a false positive on the test is 0.008 and a false negative is 0.15, what is the probability that a person who tested positive actually has TB?

the probability that a person who tested positive actually has TB is 0.64

Step-by-step explanation:

lets say

T : has tuberculosis

+ : test results +ve

- : test result is -ve

so given that

P(+ITc) = 0.008

P(-ITc) = 0.15

P(T) = 50/3000 = 1/60

P(Tc) = 1 - P(T) = 1 - 1/60 = 59/60

Now required probability

= P(TI+)

P(T∩+) / P(+)

=  P(T) × P(+IT) / [[P(T) × P(+IT)] + [(P(Tc) × P(+ITc)]

=  P(T) × {1-P(-IT)] / [[P(T) × [1-P(-IT)] + [(P(Tc) × P(+ITc)]

WE SUBSTITUTE

=  { 1/60 × (1-0.15) } /  [1/60 × (1 - 0.15)] + [(59/60) × 0.008]

= (0.0167 × 0.85) /  [(0.0167 × 0.85) + (0.9833 × 0.008)]

= 0.01417 / 0.02206

= 0.6423 ≈ 0.64

∴ the probability that a person who tested positive actually has TB is 0.64

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form

2x + 8

step-by-step explanation: