Question

what is the probability of flipping tails on the coin and spinning a 2 on the spinner? 1/8 1/7 1/4 1/2

Explanation:

Step1: Probability of flipping tails

A fair - coin has 2 possible outcomes (heads and tails). The probability of flipping tails, $P(T)$, is $\frac{1}{2}$ since there is 1 favorable outcome (tails) out of 2 total outcomes.

Step2: Probability of spinning a 2 on the spinner

The spinner has 4 possible outcomes (1, 2, 3, 4). The probability of spinning a 2, $P(2)$, is $\frac{1}{4}$ since there is 1 favorable outcome (2) out of 4 total outcomes.

Step3: Probability of both events

Since the coin - flip and the spinner - spin are independent events, the probability of both events occurring is the product of their individual probabilities. Using the formula $P(A\cap B)=P(A)\times P(B)$, where $A$ is the event of flipping tails and $B$ is the event of spinning a 2. So $P(T\cap2)=\frac{1}{2}\times\frac{1}{4}=\frac{1}{8}$.

Answer:

$\frac{1}{8}$