On the leeward side of the island of Oahu, in a small village, about 74% of the residents are of Hawaiian ancestry. Let n = 1, 2, 3, … represent the number of people you must meet until you encounter the first person of Hawaiian ancestry in the village. (a) Write out a formula for the probability distribution of the random variable n. (Enter a mathematical expression.) P(n) = (b) Compute the probabilities that n = 1, n = 2, and n = 3. (For each answer, enter a number. Round your answers to three decimal places.) P(1) = 0.740 P(2) = 0.192 P(3) = 0.050 (c) Compute the probability that n ≥ 4. Hint: P(n ≥ 4) = 1 − P(n = 1) − P(n = 2) − P(n = 3). (Enter a number. Round your answer to three decimal places.) 0.018 (d) What is the expected number of residents in the village you must meet before you encounter the first person of Hawaiian ancestry? Hint: Use μ for the geometric distribution and round. (Enter a number. Round your answer to the nearest whole number.) residents

Kindly check explanation

Step-by-step explanation:

Given that:

Probability distribution of a random variable n :

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

p = 0.74

P(n) = (1 - 0.74)^(n-1) * 0.74

P(n) = (0.74)0.26^n-1

Compute the probabilities that n = 1, n = 2, and n = 3.

n = 1

P(1) = (0.74)0.26^1-1

= 0.74 * 0.26^0

= 0.74

n = 2

P(2) = (0.74)0.26^2-1

= 0.74 * 0.26^1

= 0.74 * 0.26

= 0.192

n = 3

P(3) = (0.74)0.26^3-1

= 0.74 * 0.26^2

= 0.74 * 0.0676

= 0.050

Compute the probability that n ≥ 4.

P(n ≥ 4) = 1 - p(n ≤ 3)

p(n ≤ 3) ; n = 1, n = 2, n = 3

p(n = 1) = 0.74

p(n = 2) = 0.192

p(n = 3) = 0.050

P(n ≥ 4) = 1 - (0.74 + 0.192 + 0.050)

P(n ≥ 4) = 1 - 0.982

P(n ≥ 4) = 0.018

(d) What is the expected number of residents in the village you must meet before you encounter the first person of Hawaiian ancestry?

Expected number of residents (μ) :

μ = (1 - p) / p

p = 0.74

μ = (1 - 0.74) / 0.74

μ = 0.26 / 0.74

μ = 0.35

the answer is a i belaeve atleast thats what my calculator just gfave me

step-by-step explanation:

in the attachment.   i didn't see your choices.   the word which means there is choices.

step-by-step explanation:

(x,y)

x tells you how much left or right you go from the origin

y tells you how much down or up you go from the origin

so for example (-3,2), you go left 3 and up twice. i denoted which of the ordered pairs is which in my graph.