This is math2326, ask about probabilty

Question

Number of Storms 0 1 2 3 4 5 6 Probability .25 .33 .24 .11 .04 .02 .01 a. What is the probability of more than 2 but less than 5 snowstorms? b. Given this a particularly cold year (in which 2 snowstorms have already been observed), what is the conditional probability that a total of 4 or more snowstorms will be observed? c. What is the probability that there are 7 or more snowstorms in the year?

Answer 1

Check: probabilities total to 1, so all eventualities are covered.

a) We need to add the probabilities of 3 and 4 storms=0.11+0.04=0.15.

b) Given that there have already been two storms, the probability of 4 more storms means 6 storms in total. Let A=0.01 be the probability that 6 storms will occur and B=0.24 be the probability that 2 storms would occur. The probability that 6 storms will occur given that 2 have already occurred=

P(A⋂B)/P(B)=0.1/0.24=5/12=0.42 approx. because P(A⋂B)=P(A) since A includes B (6 storms includes there being 2 storms).

c) The total of all the given probabilities=1, so there is no probability for 7 storms. P(7)=0.