Answer:
56 Cola-flavored gumballs remaining.
Step-by-step explanation:
There are 180 gumballs. Bob purchased 40 gumballs, which leaves 140 gumballs remaining.
There are four flavors. This is the chance (shown as a percentage) of each flavor Bob recieved:
║GR: 4 ⇒ 10%
║CH: 12 ⇒ 30%
║CO: 16 ⇒ 40%
║OR: 8 ⇒ 20%
So, how can we predict the number of Cola flavored gumballs remaining?
[<em>There is a 40% chance of getting a Cola-flavored gumball from the machine. If we find 40% of 140, we can predict that is close to the number of Cola gumballs left in the machine</em>]
║0.40 ⋅ 140 = 56
40% of 140 is 56, so we can predict there are 56 Cola-flavored gumballs remaining.
Answer:
(a) 0.139258
(b) 0.0064827
Step-by-step explanation:
Let the probability that each member makes a correct decision be
and the probability that each member makes an incorrect decision be
.
From the question, ![p = 0.7](https://tex.z-dn.net/?f=p%20%3D%200.7)
p and q are mutually exclusive. Hence,
![p+q = 1](https://tex.z-dn.net/?f=p%2Bq%20%3D%201)
![q = 1 - p=1-0.7 = 0.3](https://tex.z-dn.net/?f=q%20%3D%201%20-%20p%3D1-0.7%20%3D%200.3)
(a) For majority rule, it means at least 4 members decisions are taken. Taking "C" to mean "correct" and "I" to mean "incorrect", we could have 4C against 3I, 5C against 2I, 6C against 1I and 7C against 0I.
The probability of the correct decision being made is
![P(\ge\text{4C}) = P(\text{4C and 3I}) + P(\text{5C and 2I}) +P(\text{6C and 1I}) +P(\text{7C and 0I})](https://tex.z-dn.net/?f=P%28%5Cge%5Ctext%7B4C%7D%29%20%3D%20P%28%5Ctext%7B4C%20and%203I%7D%29%20%2B%20P%28%5Ctext%7B5C%20and%202I%7D%29%20%20%20%2BP%28%5Ctext%7B6C%20and%201I%7D%29%20%2BP%28%5Ctext%7B7C%20and%200I%7D%29)
![P(\ge\text{4C}) = (0.7^4\times0.3^3)+(0.7^5\times0.3^2)+(0.7^6\times0.3^1)+(0.7^7\times0.3^0)](https://tex.z-dn.net/?f=P%28%5Cge%5Ctext%7B4C%7D%29%20%3D%20%280.7%5E4%5Ctimes0.3%5E3%29%2B%280.7%5E5%5Ctimes0.3%5E2%29%2B%280.7%5E6%5Ctimes0.3%5E1%29%2B%280.7%5E7%5Ctimes0.3%5E0%29)
![P(\ge\text{4C}) = 0.0064827 + 0.0151263 + 0.0352947 + 0.0823543 = 0.139258](https://tex.z-dn.net/?f=P%28%5Cge%5Ctext%7B4C%7D%29%20%3D%20%200.0064827%20%2B%200.0151263%20%2B%200.0352947%20%2B%200.0823543%20%3D%200.139258)
(b) ![P(\text{exactly 4C}) = P(\text{4C and 3I}) = 0.7^4\times0.3^3 = 0.0064827](https://tex.z-dn.net/?f=P%28%5Ctext%7Bexactly%204C%7D%29%20%3D%20P%28%5Ctext%7B4C%20and%203I%7D%29%20%3D%200.7%5E4%5Ctimes0.3%5E3%20%3D%200.0064827)
Answer:
jimmy cho
Step-by-step explanation: