Every day of spring the probability that a thunderstorm takes place in Toronto is 0,005. We...

Every day of spring the probability that a thunderstorm takes place in Toronto is 0,005. We assume that the events are independent and that the spring starts March 21st.

1) What is the probability that the third storm takes place May 1st?

2) What is the probability that the third storm takes place May 1st knowing that it is April 15th and a storm has just occurred the first time this Spring?

Solutions

Expert Solution

Probabilty that a thunderstorm takes place in Torronto is 0.005

we have to find probability that the third storm takes place May 1st

since the events can be considered as independent events and probability is same for every day, we can use negative binomial distribution.(otherwise we can't use it)

Negative binomial distribution is the distribution of the number of trails (or failures ) needed to get the kth success

Its pmf is given as

where k is the number of successes,r is the number of failures and p is the probability of success

Here we have to find probability of 3rd storm. so k=3

r is number of days from march 21 st to may 1st

r=42 and p=0.005

probabilty that the 3rd storm takes palce in may 1st is

=0.00134

b)Since the events are independent, probability that 3rd storm takes place May 1st knowing that the first storm has occured on April 15 th is same as the probability that it occur on May 1st without knowing when it first occured.

If A and B are two independent event, P(A|B) =P(A)

orchestra answered 1 year ago

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