Question

On the spinner, the probability of landing on black is 1/2 , and the probability of landing on red is 1/3. Create a probability distribution for the experiment of spinning the spinner.

Answer 1

Answer:

1) $p_i \geq 0 , \forall i$

2)$\sum_{i=1}^n P_i = 1, i =1,2,...,n$

And for this case we have:

$\frac{1}{2}+\frac{1}{6}= \frac{2}{3}$

By the complement rule we can find the probability that the spinner land in a non black or red space:

$p(N) = 1- \frac{1}{2} -\frac{1}{3}= \frac{1}{6}$

And then the probability distribution would be:

Color      Red     Black    N

Prob.      1/3         1/2       1/6

Step-by-step explanation:

For this case we have two possible outcomes for the spinner experiment:

$p(black) =\frac{1}{2}$

$p(red) = \frac{1}{3}$

In order to have a probability distribution we need to satisfy two conditions:

1) $p_i \geq 0 , \forall i$

2)$\sum_{i=1}^n P_i = 1, i =1,2,...,n$

And for this case we have:

$\frac{1}{2}+\frac{1}{6}= \frac{2}{3}$

By the complement rule we can find the probability that the spinner land in a non black or red space:

$p(N) = 1- \frac{1}{2} -\frac{1}{3}= \frac{1}{6}$

And then the probability distribution would be:

Color      Red     Black    N

Prob.      1/3         1/2       1/6