Probability of a cloudy day is .55 Probability of a sunny day is .45 A

1.	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» 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) = $^{4}C_1 (0.45)^{1} (1-0.45)^{4-1}$ = $40.450.55^{3}$ = 0.2995 or 0.30 Therefore, probability that exactly 1 out of 4 consecutive days will be sunny is 0.2995 ≈ 0.30 .

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»

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 .