A die is rolled and a coin is tossed, find the probability that the die shows a number less than 5 and the coin shows a head?

There are 4 numbers less than 5 on a standard six-sided die (1, 2, 3, 4) and 2 possible outcomes for the coin toss (head or tail).

The total number of possible outcomes when rolling a die and tossing a coin is 6 (for the die) x 2 (for the coin) = 12.

The number of favorable outcomes where the die shows a number less than 5 and the coin shows a head is 4 (for the die) x 1 (for the coin) = 4.

Therefore, the probability of the die showing a number less than 5 and the coin showing a head is 4/12 = 1/3 or approximately 0.3333.

The probability of rolling a number less than 5 on a die is 4/6 = 2/3.

The probability of getting a head on a coin toss is 1/2.

Since these events are independent, the probability of both happening is:

(2/3) - (1/2) = 1/3 = 0.333