Question

1. Let C be the event that a computer crashed and O the event that a computer overheated. Suppose we have the following probabilities P(C) 0.4 P(O)-0.3 P(C n O) = 0.25 P(c n O') P(C'no) 0.05 P(C" n O') 0.15 0.55 Answer the questions below, Round your answers below to 2 decimals. (a) Find the probability that the computer crashed, given that the computer overheated D) Feit eke probahillht th overheat (c) Find the probability that the computer did not overheat, given that the computer did not crash. (d) Are the events of a computer crashing and a computer overheating independent events? Explain

Answer 1

1)

a)

Required probability = $P(C|O)=\frac{P(C\cap O)}{P(O)}=\frac{0.25}{0.3}=0.83$

b)

Required probability = $P(C|O')=\frac{P(C\cap O')}{P(O')}=\frac{0.15}{1-0.3}=0.21$

c)

Required probability = $P(O'|C')=\frac{P(O'\cap C')}{P(C')}=\frac{0.55}{1-0.4}=0.92$

d)

Now, $P(C\cap O)=0.25 \neq P(C)\times P(O)$

Thus the two events are not independent.