Question

A coin is flipped and a spinner is spun. What is the probability of tails and a consonant (B or C)?

Answer 1

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:

`P(\text{tails and consonant)=P(tails)xP(consonant)}`

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:

`P(\text{tails)}=(1)/(2)`

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:

`P(\text{consonant)}=(2)/(3)`

Now, we substitute in the formula for both events and we get:

`P(\text{tails and consonant)=}(1)/(2)*(2)/(3)`

Solving the operations we get:

`P(\text{tails and consonant)=}(1)/(3)`

Therefore, the probability is 1/3 or 0.33 or 33.33%.