Answer:
Answer is first option [tex]\dfrac{2}{9}.[/tex]
Step-by-step explanation:
Let A be the event of spinning a number.
P(A) be the probability of spinning a number.
Here, total numbers in the game are 8.
Let B be the event of spinning a letter.
P(B) be the probability of spinning a letter.
Total number of letters is 4.
Total number of possibilities of a spin is 12.
Formula for probability of an event E can be observed as:
[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}[/tex]
[tex]\Rightarrow P(A) = \dfrac{8}{12}\\ \Rightarrow P(A) = \dfrac{2}{3}[/tex]
Similarly
[tex]P(B) = \dfrac{4}{12}\\\Rightarrow P(B) = \dfrac{1}{3}[/tex]
Here, events A and B are independent events and we have to find the probability of occurrence of both together. i.e. To find the probability of spinning a letter after a number.
Required probability can be achieved just by multiplying the probabilities of both the events.
[tex]\Rightarrow P(A)\times P(B)\\\Rightarrow \dfrac{2}{3} \times \dfrac{1}{3}\\\Rightarrow \dfrac{2}{9}[/tex]
So, answer is first option [tex]\dfrac{2}{9}[/tex].
