Statistics question about random probability Cheese pastureized or Raw MilkA cheese can be classified as either raw-milk or pasteurized. 82% of cheeses are classified as pasteurized. (a) Two cheeses are chosen at random. What is the probability that both cheeses are pasteurized? (b) Four cheeses are chosen at random. What is the probability that all four cheeses are pasteurized? (c) What is the probability that at least one of four randomly selected cheeses is raw-milk? Would it be unusual that at least one of four randomly selected cheeses is raw-milk? (a) The probability is . (Round to four decimal places as needed.) (b) The probability is . (Round to four decimal places as needed.) (c) The probability is D. (Round to four decimal places as needed.) It would not be unusual be unusual that at least one of four randomly selected cheeses is raw-milk.

(a) Two cheeses are chosen at random. the probability that both cheeses are pasteurized is Pr(PP) = 0.82 x 0.82 = 0.6724 to 4 decimal places)

(b) Four cheeses are chosen at random. The probability that all four cheeses are pasteurized is Pr() = 0.82 x 0.82 x 0.82 x 0.82 = 0.4521 to 4 decimal places

(c) What is the probability that at least one of four randomly selected cheeses is raw-milk is Pr(RPPP) Or Pr(RRPP) Or Pr(RRRP) Or Pr()

= 0.1269 to 4 decimal places

It would not be unusual that at least one of four randomly selected cheeses is raw-milk, because the probability have a value between 0 and 1

Step-by-step explanation:

If is given that 80% of the cheese is classified as pasteurized.

It then implies that 20% of the cheese is classified as Raw-milk

Probability of pasteurized cheese is 0.82(Denoted by Pr(P))

Probability of raw-milk cheese is 0.18(Denoted as Pr(R))

(a) Two cheeses are chosen at random. the probability that both cheeses are pasteurized is Pr(PP) = 0.82 x 0.82 = 0.6724 to 4 decimal places)

(b) Four cheeses are chosen at random. The probability that all four cheeses are pasteurized is Pr() = 0.82 x 0.82 x 0.82 x 0.82 = 0.4521 to 4 decimal places

(c) What is the probability that at least one of four randomly selected cheeses is raw-milk is Pr(RPPP) + Pr(RRPP) + Pr(RRRP) + Pr()

(0.18 x 0.82 x 0.82 x 0.82) + (0.18 x 0.18 x 0.82 x 0.82) + (0.18 x 0.18 x 0.18 x 0.82) + (0.18 x 0.18 x 0.18 x 0.18) = 0.1269 to 4 decimal places

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.

hi how are you doing today? if you ever need just tell me

step-by-step explanation: