Answer:
The probability that the coin will show tails, the spinner will land on yellow or green (out of yellow, green, blue), and the cube will show a three is
Step-by-step explanation:
Given : Fred flips a coin, spins the spinner, and rolls a standard number cube.
To find : The probability that the coin will show tails, the spinner will land on yellow or green (out of yellow, green, blue), and the cube will show a three ?
Solution :
First we find probability one by one,
1) Flips a coin - Head, Tail
Total number of outcome = 2
Favorable outcome (getting a tail) = 1
Probability that the coin will show tails is ![P(T)=\frac{1}{2}](https://tex.z-dn.net/?f=P%28T%29%3D%5Cfrac%7B1%7D%7B2%7D)
2) Spins the spinner - yellow, green, blue
Total number of outcome = 3
Favorable outcome (land on yellow or green) = 2
Probability that the spinner will land on yellow or green ![P(S)=\frac{2}{3}](https://tex.z-dn.net/?f=P%28S%29%3D%5Cfrac%7B2%7D%7B3%7D)
3) Rolls a standard number cube - 1,2,3,4,5,6
Total number of outcome = 6
Favorable outcome (show a three) = 1
Probability that the cube will show a three ![P(C)=\frac{1}{6}](https://tex.z-dn.net/?f=P%28C%29%3D%5Cfrac%7B1%7D%7B6%7D)
The probability that the coin will show tails, the spinner will land on yellow or green (out of yellow, green, blue), and the cube will show a three is
![P=P(T)+P(S)+P(C)](https://tex.z-dn.net/?f=P%3DP%28T%29%2BP%28S%29%2BP%28C%29)
![P=\frac{1}{2}+\frac{2}{3}+\frac{1}{6}](https://tex.z-dn.net/?f=P%3D%5Cfrac%7B1%7D%7B2%7D%2B%5Cfrac%7B2%7D%7B3%7D%2B%5Cfrac%7B1%7D%7B6%7D)
![P=\frac{3+4+1}{6}](https://tex.z-dn.net/?f=P%3D%5Cfrac%7B3%2B4%2B1%7D%7B6%7D)
![P=\frac{8}{6}](https://tex.z-dn.net/?f=P%3D%5Cfrac%7B8%7D%7B6%7D)
![P=\frac{4}{3}](https://tex.z-dn.net/?f=P%3D%5Cfrac%7B4%7D%7B3%7D)
Therefore, The probability that the coin will show tails, the spinner will land on yellow or green (out of yellow, green, blue), and the cube will show a three is ![\frac{4}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B3%7D)