A coin is tossed and a number cube is rolled. What is the probability that the coin shows heads and the number cube shows 6?
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
1/2 * 1/6 = ?
To find the probability of both events occurring, we need to multiply the probability of each individual event.
1. Probability of the coin showing heads:
Assuming the coin is fair, it has two equally likely outcomes: heads or tails. Therefore, the probability of getting heads is 1/2.
2. Probability of the number cube showing 6:
A number cube, also known as a fair six-sided dice, has six equally likely outcomes: the numbers 1, 2, 3, 4, 5, or 6. Therefore, the probability of rolling a 6 is 1/6.
To find the probability of both events occurring together, we multiply the probabilities:
P(coin shows heads and number cube shows 6) = P(coin shows heads) * P(number cube shows 6)
P(coin shows heads and number cube shows 6) = (1/2) * (1/6)
P(coin shows heads and number cube shows 6) = 1/12
So, the probability that the coin shows heads and the number cube shows 6 is 1/12.