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A coin is flipped and a spinner is spun simultaneously. The spinner is divided into six equally sized sections labeled with 1, 2, 3, 4, 5, 6. What is the probability of flipping a tail and landing on 5? Express your answer as a fraction in simplified form.(1 point)

1 answer

To find the probability of flipping a tail and landing on 5, we analyze the two events separately: flipping a coin and spinning the spinner.

  1. Coin Flip: There are two possible outcomes when flipping a coin: heads (H) and tails (T). The probability of flipping a tail is: \[ P(\text{T}) = \frac{1}{2} \]

  2. Spinner Spin: The spinner has six equally sized sections labeled 1 through 6. The probability of landing on the number 5 is: \[ P(5) = \frac{1}{6} \]

  3. Combined Probability: Since the coin flip and the spinner spin are independent events, we can find the combined probability of both events occurring by multiplying their individual probabilities: \[ P(\text{T and 5}) = P(\text{T}) \times P(5) = \frac{1}{2} \times \frac{1}{6} = \frac{1}{12} \]

Thus, the probability of flipping a tail and landing on 5 is: \[ \boxed{\frac{1}{12}} \]