Question

The Weather Channel’s forecasts are accurate about 75% of the time. Suppose the five-day forecast was given.

a. What is the probability that the forecast will be correct for exactly 4 days out of 5?

b. What is the probability that the forecast will be correct for at least 3 days out of 5?

     

Answer 1

Answer)

As there are fixed number of trials and probability of each and every trial is same and independent of each other

Here we need to use the binomial formula

P(r) = ncr*(p^r)*(1-p)^n-r

Ncr = n!/(r!*(n-r)!)

N! = N*n-1*n-2*n-3*n-4*n-5........till 1

For example 5! = 5*4*3*2*1

Special case is 0! = 1

P = probability of single trial = 0.75

N = number of trials = 5

R = desired success

A)

P(4) = 5c4*(0.75^4)*(1-0.75)^5-4 = 0.3955078125

B)

P(at least 3) = P(3) + P(4) + P(5) = 0.896484375