if you toss a coin and roll a number cube, what is the probability that the coin shows tails and the number cube shows 4?
prob(tails and 4)
= (1/2)(1/6)
= 1/12
To calculate the probability of two independent events happening together, you need to multiply their individual probabilities.
For a fair coin, there are two equally likely outcomes: heads and tails. So the probability of getting tails is 1/2.
A number cube, also known as a standard six-sided die, has six equally likely outcomes: the numbers 1, 2, 3, 4, 5, and 6. So the probability of rolling a 4 is 1/6.
To find the probability of both events happening together, you multiply the individual probabilities:
Probability of getting tails on the coin (1/2) × Probability of rolling a 4 on the number cube (1/6) = 1/2 x 1/6 = 1/12.
Therefore, the probability that the coin shows tails and the number cube shows 4 is 1/12.