Respuesta :
Answer:
[tex]\text{P(spinning a 3 and choosing a red)}=\frac{3}{70}[/tex]
Step-by-step explanation:
It has been given that you are spinning a spinner labeled 1-5 and you choose a marble out of the bag of 7 marbles, 2 are blue, 3 are red, 1 is green and 1 is black.
[tex]\text{Probability}=\frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}[/tex]
The probability of spinning a 3 would be: [tex]\frac{1}{5}[/tex].
The probability of choosing a red would be:
[tex]\text{P(Red)}=\frac{\text{Number of red marbles}}{\text{Total number of marbles}}[/tex]
[tex]\text{P(Red)}=\frac{3}{7+2+3+1+1}[/tex]
[tex]\text{P(Red)}=\frac{3}{14}[/tex]
Since both events are independent, so probability of spinning a 3 and choosing a red marble would be probability of spinning a 3 times probability of choosing a red marble.
[tex]\text{P(spinning a 3 and choosing a red)}=\text{P(spinning a 3)}\times \text{P(Choosing a red)}[/tex]
[tex]\text{P(spinning a 3 and choosing a red)}=\frac{1}{5}\times \frac{3}{14}[/tex]
[tex]\text{P(spinning a 3 and choosing a red)}=\frac{1\times 3}{5\times 14}[/tex]
[tex]\text{P(spinning a 3 and choosing a red)}=\frac{3}{70}[/tex]
Therefore, the probability of spinning a 3 and choosing a red marble would be [tex]\frac{3}{70}[/tex].
