Question

Please help fast.

A number cube is rolled and a coin is tossed. The number cube and the coin are fair. What is the probability that the number rolled is greater than 4 and the coin toss is tails? Write your answer as a fraction in simplest form.

Answer 1

`(1)/(6)`

Explanation:

In probability theory, "AND" means multiplication and "OR" means "addition".

We can find the 2 probabilities separately and multiply them (as there is "AND")

So,

Probability number rolled greater than 4 = number of numbers that are greater than 4/total number of numbers

There are 2 numbers greater than 4 in a die (5 & 6) and total 6 numbers, so

P(number greater than 4) = 2/6

Now,

Probability that tails come up in coin toss = 1/2 (there are 1 tail and 1 head in a coin)

Hence,

P(number greater than 4 and tails in coin) = 2/6 * 1/2 = 1/6