A coin is tossed and a die is thrown. The probability that the outcome will be a tail on the coin or a number greater than 3 on the die is

The probability of getting a tail on the coin or a number greater than 3 on the die needs to be determined.

The coin has 2 outcomes: Head (H) or Tail (T)

The die has 6 outcomes: 1, 2, 3, 4, 5, 6

Total combined outcomes = 2 × 6 = 12

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The favorable outcomes occur when there is a tail on the coin or a number greater than 3 (that is, 4, 5, or 6) on the die.

When coin shows Tail:

(T, 1), (T, 2), (T, 3), (T, 4), (T, 5), (T, 6) → 6 outcomes

When coin shows Head and die shows a number greater than 3:

(H, 4), (H, 5), (H, 6) → 3 outcomes

Total favorable outcomes = 6 + 3 = 9

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The probability is:

$$\text{Probability} = \dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}$$Probability=Total outcomesFavorable outcomes​

$$\text{Probability} = \dfrac{9}{12}$$Probability=129​

$$\text{Probability} = \dfrac{3}{4}$$Probability=43​

Therefore, the probability that the outcome will be a tail on the coin or a number greater than 3 on the die is $\dfrac{3}{4}$43​.