Answer:
a) P{W>0} = 0.5
b) P{W<0} = 0.5
c) E[W] = 0
Step-by-step explanation:
Solution:
a) P(W > 0) is 0.5 because there is a 0.5 chance the player will win on their first gamble and stop with a net profit.
b) P(W = 0) is 0.25 because there is a 0.5 chance the player will lose on their first gamble, then also a 0.5 chance they will win on their second gamble and stop with a profit of 0.
All other combinations of gambles result in a net loss, so P(W < 0) = 1−P(W > 0)−P(W = 0)
c) The expected value can be obtained by summing the products of each profit and the probability of that profit. In this case, you have 1∗0.5+0∗0.25+(−1)∗0.125+(−2)∗0.0625, etc. So E(W) is the sum to infinity:
= (1 - n) / 2^( n + 1 )
= 0
Answer:
c
Step-by-step explanation:
divide 96 by 1.5 and you'll get 64
Answer:
x=1
Step-by-step explanation:
(15x^3- 2)^3= 2197
Take the cube root of each side
(15x^3- 2)^3 ^ 1/3= 2197^ 1/3
15x -2 = 13
Add 2 to each side
15x^3- 2+2= 13+2
15x^3 =15
Divide each side by 15
15x^3 /15 =15/15
x^3 =1
Take the cube root of each side
x^3 ^1/3 = 1^1/3
x=1
Answer:
Correct answer: x₁ = 8
Step-by-step explanation:
Given equation is:
x² - 8 = 7x ⇒ x² - 7x - 8 = 0 ⇒ x² - 8x + x - 8 = 0 ⇒ x ·(x - 8) + (x - 8) = 0
(x - 8) · (x + 1) = 0 ⇒ x₁ = 8 or x₂ = -1
we accept a positive solution
x₁ = 8
God is with you!!!