We are given that a coin is flipped a spinner spun and we are asked about the probability of getting tails and a consonant. To do that we will use the following formula for combined probabilities of independent events:
[tex]P(\text{tails and consonant)=P(tails)xP(consonant)}[/tex]Therefore, the combined probability is the product of both probabilities.
Now we determine each of the probabilities. The probabilities of getting tails is the number of desired outcomes which is 1 (tails) and the total number of outcomes in this case 2 (heads, tails), therefore, the probability is:
[tex]P(\text{tails)}=\frac{1}{2}[/tex]Now, the probability of getting a consonant is the number of desired events which is 2 ( B or C), and the total number of possible events which is (A, B, or C). Therefore, the probability is:
[tex]P(\text{consonant)}=\frac{2}{3}[/tex]Now, we substitute in the formula for both events and we get:
[tex]P(\text{tails and consonant)=}\frac{1}{2}\times\frac{2}{3}[/tex]Solving the operations we get:
[tex]P(\text{tails and consonant)=}\frac{1}{3}[/tex]Therefore, the probability is 1/3 or 0.33 or 33.33%.