$1
because 2 months is 25. so 8 months divided by 2 is 4 so 4 times 25. is 1 dollar
Answer:
![P[at\ least\ 1] = 0.9961](https://tex.z-dn.net/?f=P%5Bat%5C%20least%5C%201%5D%20%3D%200.9961)
Step-by-step explanation:
Given


Required
Probability that s/he gets at least one correctly
First, we calculate the probability of answering a question correctly
Since, there are just 2 choices (true or false), the probability is:

Similarly, the probability of answering a question, wrongly is:

The following relationship exists, in probability:
![P[at\ least\ 1] = 1 - P[none]](https://tex.z-dn.net/?f=P%5Bat%5C%20least%5C%201%5D%20%3D%201%20-%20P%5Bnone%5D)
So, to calculate the required probability.
First, we calculate the probability that he answers none of the 8 questions correctly.
![P[none] = p(wrong)^8](https://tex.z-dn.net/?f=P%5Bnone%5D%20%3D%20p%28wrong%29%5E8)
![P[none] = (\frac{1}{2})^8](https://tex.z-dn.net/?f=P%5Bnone%5D%20%3D%20%28%5Cfrac%7B1%7D%7B2%7D%29%5E8)
Substitute
in ![P[at\ least\ 1] = 1 - P[none]](https://tex.z-dn.net/?f=P%5Bat%5C%20least%5C%201%5D%20%3D%201%20-%20P%5Bnone%5D)
![P[at\ least\ 1] = 1 - (\frac{1}{2})^8](https://tex.z-dn.net/?f=P%5Bat%5C%20least%5C%201%5D%20%3D%201%20-%20%28%5Cfrac%7B1%7D%7B2%7D%29%5E8)
![P[at\ least\ 1] = 1 - \frac{1}{256}](https://tex.z-dn.net/?f=P%5Bat%5C%20least%5C%201%5D%20%3D%201%20-%20%5Cfrac%7B1%7D%7B256%7D)
Take LCM
![P[at\ least\ 1] = \frac{256 - 1}{256}](https://tex.z-dn.net/?f=P%5Bat%5C%20least%5C%201%5D%20%3D%20%5Cfrac%7B256%20-%201%7D%7B256%7D)
![P[at\ least\ 1] = \frac{255}{256}](https://tex.z-dn.net/?f=P%5Bat%5C%20least%5C%201%5D%20%3D%20%5Cfrac%7B255%7D%7B256%7D)
![P[at\ least\ 1] = 0.9961](https://tex.z-dn.net/?f=P%5Bat%5C%20least%5C%201%5D%20%3D%200.9961)
<em></em>
<em>Hence, the probability that s/he gets at least one correctly is 0.9961</em>
Answer:
PArt 1: 4/40 (not simplified) 1/10 (simplified)
Part 2: 8/40 (not simplified) 2/10 (simplified)
Step-by-step explanation:
add all the marbles together and you get 40. there are 4 colors in the jar but with different amounts, you will divide 40 into each amount of marbles (example: 40/4 = 10 = there are 4 10s in 40).
3×4 =12.
12-2 =10
You will have 10