What is the probability of rolling cube and getting a 4 and then an even number?

A. 1/6
B. 1/2**
C. 1/12
D. 2/3

A coin is tossed and a number cube is rolled. What is P(heads, a number less than 5)?

A 1/3
B 5/12
C 2/3
D 5/6

First question: try again

Second question: try

1. I don't know, sorry.

2. 1/3

To calculate the probability of rolling a specific outcome on a cube (e.g., rolling a 4) and then rolling an even number, you need to determine the probability of each event occurring individually and then multiply them together.

There are six possible outcomes when rolling a standard six-sided cube, each with a 1/6 probability of occurring because all sides are equally likely. So, the probability of rolling a 4 is 1/6.

For the second event, rolling an even number, there are three possible outcomes - 2, 4, and 6 - which all have an equal probability of 1/6. However, we want to find the probability of rolling an even number after already rolling a 4, so we need to consider the remaining outcomes. Since the 4 has already been rolled, there are only two remaining even numbers (2 and 6), giving us a 2/6 probability.

To find the overall probability of both events occurring, we multiply the individual probabilities together: (1/6) * (2/6) = 1/18.

Therefore, the correct choice is C. 1/12.

For the second question, the situation involves both a coin toss and rolling a number cube. Again, you need to determine the probability of each event occurring individually and then multiply them together.

When flipping a fair coin, there are two possible outcomes - heads or tails - each with a 1/2 probability of occurring.

When rolling a number cube, there are six possible outcomes, each with an equal 1/6 probability of occurring.

To find the probability of getting heads and a number less than 5, you need to consider the overlapping possibilities. Specifically, the number cube outcome needs to be less than 5 at the same time as the coin shows heads.

The possible outcomes that satisfy these conditions are: heads (H), 1, 2, 3, and 4. Out of these five outcomes, four (H, 1, 2, 3) meet the requirement. Thus, the probability is 4 out of 12, or 4/12, which simplifies to 1/3.

Therefore, the correct choice is A. 1/3.