Question

Let E and F be two events of an experiment with sample space S. Suppose P(E) = 0.2, P(F) = 0.1 and P(E n F) = 0.05. Compute.

a.      P(E u F)

b.     P(E^c n F^c)

c.      P(E n F)

Answer 1

a.

$$P(E\cup F)=P(E)+P(F)-P(E\cap F)$$

$$P(E\cup F)=0.2+0.1-0.05=0.25$$

b.

$$P(E^C\cap F^C)=1-P(E\cup F)$$

$$P(E^C\cap F^C)=1-0.25=0.75$$

c.

$$P(E^C\cup F^C)=P(E^C)+P(F^C)-P(E^C\cap F^C)$$

$$=1-P(E)+1-P(F)-P(E^C\cap F^C)$$

$$P(E^C\cup F^C)=1-0.2+1-0.1-0.75=0.95$$

$$P(E^C\cup F^C)=1-P(E\cap F)$$

$$P(E^C\cup F^C)=1-0.05=0.95$$