Question

A number cube is rolled and a coin is flipped.find the probabilities below

Answer 1

The two events are independent, because the result of the number cube has no influence on the coin flipped, and vice versa. So, we can calculate the two probabilities independently and then multiply them.

So, we have:

P(1 and heads) = P(cube returns 1) * P(coin returns heads)

The probability of rolling 1 is 1/6, because there are 6 numbers on the cube, and they all have the same probability. Similarly, the probability of getting heads is 1/2, because it's either heads or tails with equal probability.

$P(\text{1 and heads}) = \dfrac{1}{6}\cdot\dfrac{1}{2}=\dfrac{1}{12}$

The other two exercises follow the exact same logic, you only need to count how many outcomes satisfy your request for both the cube and the coin, and multiply the probabilities:

$P(\text{even and tails})=\dfrac{1}{2}\cdot\dfrac{1}{2}=\dfrac{1}{4}$

$P(\text{5 or 6 and heads})=\dfrac{2}{6}\cdot\dfrac{1}{2}=\dfrac{1}{6}$