1. a coin is tossed, and a standard number cube is rolled. what is the probability that the coin lands heads and the cube rolls an even number?
1/2 * 3/6 = 1/4
To determine the probability that the coin lands heads and the cube rolls an even number, we need to first find the probabilities of each event separately, and then multiply them together.
1. Probability of the coin landing heads:
Since there are two equally likely outcomes (heads or tails) when flipping a fair coin, the probability of landing heads is 1/2 or 0.5.
2. Probability of the cube rolling an even number:
A standard number cube has six sides numbered 1 to 6. Out of these six numbers, three are even (2, 4, and 6). So, the probability of rolling an even number is 3/6 or 1/2.
Now, we multiply the probabilities together:
Probability of coin landing heads * Probability of cube rolling an even number
= 0.5 * 0.5
= 0.25
Therefore, the probability that the coin lands heads and the cube rolls an even number is 0.25 or 1/4.
To determine the probability that the coin lands heads and the cube rolls an even number, we need to find the individual probabilities of each event happening and then multiply them together.
Step 1: Determine the probability of the coin landing heads.
Since a standard coin has only two sides (heads and tails) and these sides are equally likely to occur, the probability of the coin landing heads is 1/2, or 0.5.
Step 2: Determine the probability of the cube rolling an even number.
A standard number cube has six sides numbered from 1 to 6, with three of them being even numbers (2, 4, and 6). So, the probability of rolling an even number on a cube is 3/6, which simplifies to 1/2, or 0.5.
Step 3: Multiply the probabilities together.
To find the probability of both events occurring, we multiply the probabilities determined in Step 1 and Step 2:
0.5 * 0.5 = 0.25.
Therefore, the probability that the coin lands heads and the cube rolls an even number is 0.25, or 25%.