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In a multiple choice quiz, there are 5 questions each with 4 answer choices (a, b, c, and d). Robin has not studied for the quiz

k0ka [10]

Answer:

A. 0.1035

B. 0.1406

C. 0.1025

Step-by-step explanation:

Given that:

the number of sample questions (n) = 5

The probability of choosing the correct choice (p) = 1/4 = 0.25

Suppose X represents the number of question that are guessed correctly.

Then, the required probability that she gets the majority of her question correctly is:

P(X>2) = P(X=3) + P(X =4) + P(X = 5)

$P(X>2) = [ (^{5}C_{3}) \times (0.25)^3 (1-0.25)^{5-3} + (^{5}C_{4}) \times (0.25)^4 (1-0.25)^{5-4} + (^{5}C_{5}) \times (0.25)^5 (1-0.25)^{5-5}$

$P(X>2) = \Bigg [ \dfrac{5!}{3!(5-3)!} \times (0.25)^3 (1-0.25)^{2} + \dfrac{5!}{4!(5-4)!} \times (0.25)^4 (1-0.25)^{1} +\dfrac{5!}{5!(5-5)!} \times (0.25)^5 (1-0.25)^{0} \Bigg ]$

P(X>2) = [ 0.0879 + 0.0146 + 0.001 ]

P(X>2) = 0.1035

B.

Recall that

n = 5 and p = 0.25

The probability that the first Q. she gets right is the third question can be computed as:

$P(X=x) = 0.25 ( 1- 025) ^{x-1}$

Since, x = 3

$P(X = 3) = 0.25 ( 1- 0.25 ) ^{3-1}$

$P(X =3) = 0.25 (0.75)^{3-1}$

$P(X =3) = 0.25 (0.75)^{2}$

P(X=3) = 0.1406

C.

The probability she gets exactly 3 or exactly 4 questions right is as follows:

P(X. 3 or 4) = P(X =3) + P(X =4)

$P(X=3 \ or \ 4) = [ (^{5}C_{3}) \times (0.25)^3 (1-0.25)^{5-3} + (^{5}C_{4}) \times (0.25)^4 (1-0.25)^{5-4}]$

$P(X=3 \ or \ 4) = \Bigg [ \dfrac{5!}{3!(5-3)!} \times (0.25)^3 (1-0.25)^{2} + \dfrac{5!}{4!(5-4)!} \times (0.25)^4 (1-0.25)^{1} \Bigg ]$

P(X = 3 or 4) = [ 0.0879 + 0.0146 ]

P(X=3 or 4) = 0.1025

3 0

3 years ago

Y

hichkok12 [17]

Answer:

the correct ones are the 1st, 3rd and 4th

the range is (0:+infinity)

and the second statemend is false because 2²=4, but 2³=8, and 8=4=4 not 2

3 0

3 years ago

The cost of strawberries if they are $2 per pound the subject is translating expressions

Gekata [30.6K]

Answer:

2(equation)

Step-by-step explanation: multiply the equation by 2 to get the price

3 0

3 years ago

What are the solutions of the equation x4 - 5x2 - 14 = 0? Use factoring<br> to solve.

stellarik [79]

Answer:

x = ±√7, ±i√2

Step-by-step explanation:

$x^4-5x^2-14=0\\(x^2-7)(x^2+2)=0\\$

$x^2 - 7 = 0$ or $x^2 + 2 = 0\\$

x^2 - 7 = 0

x^2 = 7

x = ±√7

or x^2 + 2 = 0

x^2 = -2

x = ±i√2

6 0

2 years ago

Suppose a regular pentagon with a perimeter of 34 inches was dilated by a scale factor of 0.25. Fill in the blanks in the follow

rusak2 [61]

Answer:

$6.8\ \text{in}$

$8.5\ \text{in}$

$1.7\ \text{in}$

Step-by-step explanation:

Perimeter of the pendulum = 34 inches

Scale factor = 0.25

x = Length of side of pentagon

$5x=34\\\Rightarrow x=\dfrac{34}{5}\\\Rightarrow x=6.8\ \text{in}$

The pentagon’s side length before the dilation was $6.8\ \text{in}$ .

New perimeter of the pentagon

$34\times 0.25=8.5\ \text{in}$

New perimeter of the pentagon is $8.5\ \text{in}$ .

$5x=8.5\\\Rightarrow x=\dfrac{8.5}{5}\\\Rightarrow x=1.7\ \text{in}$

The new side length of the perimeter is $1.7\ \text{in}$ .

7 0

3 years ago