Answer:
0.3333 = 33.33%
Step-by-step explanation:
We have 2 vacancies that will be filled from among 10 people, so the number of combinations we have is a combination of 10 choose 2, which is 10*9/2 = 45 possibilities.
Among these possibilities, the cases where the 2 vacancies are occupied by men is:
We have 6 men for 2 vacancies, so is a combination of 6 choose 2, which is 6*5/2 = 15 cases.
From the 45 cases we have, 15 are cases that no woman was selected, so the probability that no woman is selected is 15/45 = 1/3 = 0.3333 = 33.33%
Writing this statement symbolically, we get:
n
--- - 5 = 8
2
Adding 5 to both sides, we get n/2 = 13. Then n = 26.
Because the actual dimensions of the board and the target are missing, let us supply the missing values.
Let:
radius of board = 6 inches
radius of target = 2 inches
Area of board = pi * r^2 = pi*6^2 = 36pi
Area of target = pi * r^2 = pi*2^2 = 4pi
Probability of hitting the target = 4pi / 36pi = 1/9
Therefore, there is a 1/9 chance of hitting the target on the board.
- 15 ![\frac{13}{15}](https://tex.z-dn.net/?f=%5Cfrac%7B13%7D%7B15%7D)
change the mixed numbers to improper fractions
2
= ![\frac{14}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B14%7D%7B5%7D)
5
= ![\frac{17}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B17%7D%7B3%7D)
multiply the improper fractions
× - ![\frac{17}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B17%7D%7B3%7D)
= -
= -
= - 15 ![\frac{13}{15}](https://tex.z-dn.net/?f=%5Cfrac%7B13%7D%7B15%7D)