Mathematics, 03.12.2019 02:31 panishreyashi

You roll a fair die three times. what is the probability of each of the following?
a) you roll all 4's.
b) you roll all even numbers.
c) none of your rolls gets a number divisible by 2.
d) you roll at least one 2.
e) the numbers you roll are not all 2's.

Answers: 2

Show answers

Answers

Answer from: lovehelping7095

(a) $\frac{1}{216}$

(b) $\frac{1}{8}$

(d) $\frac{191}{216}$

(e) $\frac{215}{216}$

Step-by-step explanation:

It is given that we roll a fair die three times. We need to find the following probability.

Total possible value = 1,2,3,4,5,6

(a) You roll all 4's.

Probability of getting a 4 = $\frac{1}{6}$

Probability of getting 4 on all rolls = $\frac{1}{6}\times \frac{1}{6}\times \frac{1}{6}=\frac{1}{216}$

Therefore, the probability of getting 4 on all rolls is $\frac{1}{216}$ .

(b) You roll all even numbers.

Even number = 2,4,6

Probability of getting an even number $=\frac{3}{6}=\frac{1}{2}$

Probability of getting even number on all rolls = $\frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}=\frac{1}{8}$

Therefore, the probability of getting even number on all rolls is $\frac{1}{8}$ .

odd number = 1,3,5

Probability of getting an odd number $=\frac{3}{6}=\frac{1}{2}$

Probability of getting odd number on all rolls = $\frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}=\frac{1}{8}$

Therefore, the probability of getting odd number on all rolls is $\frac{1}{8}$ .

(d) You roll at least one 2.

Probability of getting a 2 = $\frac{1}{6}$

Probability of getting any number except 2 = $\frac{5}{6}$

Probability of getting any number except 2 in all rolls = $\frac{5}{6}\times \frac{5}{6}\times \frac{5}{6}=\frac{125}{216}$

Probability of getting at least one 2 = 1 - P(getting no 2)

Probability of getting at least one 2 = $1-\frac{125}{216}=\frac{191}{216}$

Therefore, the probability of getting at least one 2 is $\frac{191}{216}$ .

(e) The numbers you roll are not all 2's.

Probability of getting a 2 = $\frac{1}{6}$

Probability of getting all 2 = $\frac{1}{6}\times \frac{1}{6}\times \frac{1}{6}=\frac{1}{216}$

Probability of getting all not all 2's = $1-\frac{1}{216}=\frac{215}{216}$

Therefore, the probability of getting not all 2's is $\frac{215}{216}$ .

Answer from: Quest

d is the correct answer

step-by-step explanation:

x= 8 because 3x = 3 * 8, and 3*8 = 24

Answer from: Quest

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240

Another question on Mathematics

Mathematics, 21.06.2019 20:00

Which type of graph would allow us to quickly see how many students between 100 and 200 students were treated?

Answers: 1

Answer

Mathematics, 21.06.2019 20:30

What is the measure of angle x? answer

Answers: 1

Answer

Mathematics, 21.06.2019 23:20

1. ∠1 is complementary to ∠2 and ∠3 is complementary to ∠2. subtraction property of equality 2. m∠1 + m∠2 = 90 and m∠3 + m∠2 = 90 substitution 3. m∠1 + m∠2 = m∠3 + m∠2 definition of complementary 4. m∠1 = m∠3 given

Answers: 3

Answer

Mathematics, 22.06.2019 00:00

A6 ounce bottle of dressing costs $1.56 a 14 ounce bottle costs $3.36 a 20 ounce bottle costs $5.60 which has the lowest cost per ounce

Answers: 1

Answer

You know the right answer?

You roll a fair die three times. what is the probability of each of the following?
a) you ro...

Questions