Question

The probability that a randomly selected elementary or secondary school teacher from a city is a female is , holds a second job is , and is a female and holds a second job is . Find the probability that an elementary or secondary school teacher selected at random from this city is a female or holds a second job.

Answer 1

Answer:

The probability that an elementary or secondary school teacher selected at random from this city is a female or holds a second job is 0.90.

Step-by-step explanation:

Denote the events as follows:

X = an elementary or secondary school teacher from a city is a female

Y = an elementary or secondary school teacher holds a second job

The information provided is:

P (X) = 0.66

P (Y) = 0.46

P (X ∩ Y) = 0.22

The addition rule of probability is:

$P(A\cup B)=P(A)+P(B)-P(A\cap B)$

Use this formula to compute the probability that an elementary or secondary school teacher selected at random from this city is a female or holds a second job as follows:

$P(X\cup Y)=P(X)+P(Y)-P(X\cap Y)\\=0.46+0.66-0.22\\=0.90$

Thus, the probability that an elementary or secondary school teacher selected at random from this city is a female or holds a second job is 0.90.