Question

Probability of a cloudy day is .55 Probability of a sunny day is .45 A)What is the probability of three consecutive cloudy days, followed by a sunny day? B)What is the probability that exactly 1 out of 4 consecutive days will be sunny?

Answer 1

Answer:

A) 0.0749

B) 0.2995

Step-by-step explanation:

We are given that Probability of a cloudy day, P(C) = 0.55

                              Probability of a sunny day , P(S) = 0.45

A) Probability of three consecutive cloudy days, followed by a sunny day = Probability that first three days is cloudy day and fourth day is sunny day

    = P(C) * P(C) * P(C) * P(S) = 0.55 * 0.55 * 0.55 * 0.45

                                             = 0.0749 or 0.075 .

B) Probability that exactly 1 out of 4 consecutive days will be sunny is given by;

Let us consider this situation as of Binomial probability case in which ;

      Number of trials, n = 4

 Probability of success (sunny day), p = 0.45

      Number of success, x = 1

P(X = x) = $\binom{n}{r}p^{r}(1-p)^{n-r}$ for x = 0,1,2,3,.........

So, P(X = 1) = $^{4}C_1 (0.45)^{1} (1-0.45)^{4-1}$

                  = $4*0.45*0.55^{3}$ = 0.2995 or 0.30

Therefore, probability that exactly 1 out of 4 consecutive days will be sunny is 0.2995 ≈ 0.30 .