Suppose two houses in a thousand catch fire in a year and there are 2000 houses in a village. What is the probability

Q6. Suppose two houses in a  thousand catch fire in a year and there are 2000 houses in a village. What is the probability that: (i) none of the houses catch fire and (ii) At least one house catch fire?

Answer:

Given the probability of a house catching fire is:

p = 2/1000 = 0.0002 and n = 2000

Therefore, m = np = 2000 * 0.002 = 4

Therefore, the required probabilities are calculated as follows:

1)      The probability that none catches fire is given by:

P(x=0) = a ^–m  ( m⁰/ L0 ) = a ^-4  =  0.01832

Therefore, the probability that none of the houses catches fire is 0.01832.

2)      The probability that at least one catches fire is given by:

P(x≥1) = 1 – P(x=0) = 1 – 0.01832 = 0.98168

Therefore, the probability that at least one house catches fire is 0.98168