Spinner Outcome Probability
I have a spinner that lands on 1 with a probability of $ \frac{1}{10} $, 2 with a probability of $ \frac{2}{10} $, 3 with a probability of $ \frac{3}{10} $, and 4 with a probability of $ \frac{4}{10} $. If Phil and Sarah both spin the spinner, what is the probability that they get the same number?
- 1
- 2
- 3
- +
- 4
- 5
- 6
- -
- 7
- 8
- 9
- $\frac{a}{b}$
- .
- 0
- =
- %
- $a^n$
- $a^{\circ}$
- $a_n$
- $\sqrt{}$
- $\sqrt[n]{}$
- $\pi$
- $\ln{}$
- $\log$
- $\theta$
- $\sin{}$
- $\cos{}$
- $\tan{}$
- $($
- $)$
- $[$
- $]$
- $\cap$
- $\cup$
- $,$
- $\infty$
Solution
This problem requires a little bit of casework. There are four ways in which they can both get the same number: if they both get 1's, both get 2's, both get 3's or both get 4's. The probability of getting a 1 is $ \dfrac{1}{10} $, so the probability that they will both spin a 1 is $ \left(\dfrac{1}{10}\right)^2=\dfrac{1}{100} $. Similarly, the probability of getting a 2 is $ \dfrac{2}{10} $, so the probability that they will both spin a 2 is $ \left(\dfrac{2}{10}\right)^2=\dfrac{4}{100} $, the probability of getting a 3 is $ \dfrac{3}{10} $, so the probability that they will both get a 3 is $ \left(\dfrac{3}{10}\right)^2=\dfrac{9}{100} $ and the probability of getting a 4 is $ \dfrac{4}{10} $, so the probability that they will both get a 4 is $ \left(\dfrac{4}{10}\right)^2=\dfrac{16}{100} $. So our answer is $ \dfrac{1}{100}+\dfrac{4}{100}+\dfrac{9}{100}+\dfrac{16}{100}=\frac{30}{100}=\boxed{\dfrac{3}{10}} $.
Freeflows