tossing a coin tails up or rolling a number less than 4 on a number cube.
I got 1/2 + 3/6 and got 1.
The answer is 3/4. I don't understand what to do. Please help.
clearly the answer cannot be 1, since that would mean you always get tails or roll less than 4.
there are 12 possible outcomes, easy to list them.
1/2 give tails
1/2 * 3/6 = 1/4 gives heads and n<4.
1/2 + 1/4 = 3/4
or, consider P(heads & n>=4) = 1/2 * 1/2 = 1/4
you want 1 minus that, or 3/4.
To solve this problem, you need to determine the probability of either tossing a coin tails up or rolling a number less than 4 on a number cube.
First, let's find the probability of tossing a coin tails up. Since a fair coin has two equally likely outcomes (heads or tails), the probability of tossing a coin tails up is 1/2.
Next, let's find the probability of rolling a number less than 4 on a number cube. A standard number cube has six sides numbered 1 through 6. The numbers less than 4 on a number cube are 1, 2, and 3, which means there are three favorable outcomes out of a total of six possible outcomes. Therefore, the probability of rolling a number less than 4 on a number cube is 3/6 or simplified to 1/2.
To find the probability of either tossing a coin tails up OR rolling a number less than 4, you need to add the probabilities of each event happening.
1/2 + 1/2 = 2/2 = 1
So, based on your calculation, you correctly determined that the probability is 1. However, the correct answer is 3/4 and not 1.
To understand why, let's consider the concept of Mutually Exclusive Events. In this scenario, tossing a coin tails up and rolling a number less than 4 on a number cube are not mutually exclusive. It is possible for both events to happen at the same time (i.e., getting tails on a coin and rolling a 3 on a number cube).
To account for this, you need to subtract the probability of both events happening simultaneously from the sum of their individual probabilities. In this case, the probability of both events happening at the same time is 1/6 (since only one outcome satisfies both conditions - getting tails on a coin and rolling a 3 on a number cube).
So, the correct calculation is:
1/2 + 1/2 - 1/6 = 3/6 + 3/6 - 1/6 = 5/6
Therefore, the correct answer is 5/6 or simplified to 3/4.
To determine the probability of either event, tossing a coin tails up or rolling a number less than 4 on a number cube, we need to find the probability of each event separately and then add them together.
Let's break it down step by step:
1. Tossing a coin tails up:
- When tossing a fair coin, there are two equally likely outcomes: heads or tails.
- Since we want the probability of getting tails, which is one of the two equally likely outcomes, the probability of tails is 1/2.
2. Rolling a number less than 4 on a number cube:
- A number cube, or a standard six-sided die, has six equally likely outcomes: the numbers 1, 2, 3, 4, 5, and 6.
- Out of these six outcomes, there are three numbers (1, 2, and 3) that are less than 4.
- So, the probability of rolling a number less than 4 is 3/6 or simplified as 1/2.
Now, to find the probability of either event happening, we add the probabilities together:
1/2 (probability of tails) + 1/2 (probability of rolling a number less than 4) = 1/2 + 1/2 = 2/2 = 1.
However, the correct answer is stated as 3/4, not 1.
To understand why the answer is 3/4, we must consider that getting tails on a coin and rolling a number less than 4 on a number cube are independent events. To calculate the probability of both events occurring, we multiply their individual probabilities:
1/2 (probability of tails) x 1/2 (probability of rolling a number less than 4) = 1/4.
Therefore, the probability of either event happening is 1 - probability of neither event happening. Since getting neither tails nor a number less than 4 is the opposite of what we want:
1 - 1/4 = 3/4.
Hence, the correct answer is 3/4, not 1.