Question

Dangerous fires are rare (1%)

But smoke is fairly common(10%) due to barbecues,

And 90% of dangerous fires make smoke

We can then discover the

. probability of dangerous fire when there is smoke.

Dangerous fires are rare (1%)

But smoke is fairly common(10%) due to barbecues,

And 90% of dangerous fires make smoke

We can then discover the

. probability of dangerous fire when there is smoke.

Answer 1

Let D and S denote the events of dangerous fire and of smoke respectively

P(D) = 0.01

P(S) = 0.10

P(S | D) = 0.90

The probability of dangerous fire when there is smoke

= P(D | S)

= P(S | D)*P(D)/P(S)

= 0.90*0.01/0.10 = 0.090