You roll a number cube twice. Find the probability of the event in fraction form.
-Rolling a 4 then an even number
-Rolling a 3 then a 3
-Rolling a number less than 1 and then a number less than 2
since the events are independent, just multiply their probabilities. For the first, that would be
1/6 * 1/2
and the others likewise
To find the probability of an event, you need to determine the number of successful outcomes divided by the total number of possible outcomes.
Let's start by calculating the sample space (total number of possible outcomes) for each scenario:
1. Rolling a number cube twice:
The number cube has 6 faces, so for each roll, there are 6 possible outcomes. Since you roll it twice, the total number of possible outcomes is 6 * 6 = 36.
Now let's calculate the probability for each event:
1. Rolling a 4 then an even number:
To roll a 4 on the first attempt, there is only 1 successful outcome (rolling a 4). On the second attempt, there are 3 successful outcomes (rolling a 2, 4, or 6). Therefore, the number of successful outcomes is 1 * 3 = 3.
So the probability of rolling a 4 then an even number is 3/36.
2. Rolling a 3 then a 3:
To roll a 3 on both attempts, there is only 1 successful outcome for each roll. Therefore, the number of successful outcomes is 1 * 1 = 1.
So the probability of rolling a 3 then a 3 is 1/36.
3. Rolling a number less than 1 and then a number less than 2:
Since there is no face on the number cube that is less than 1, it is impossible to roll a number less than 1. Therefore, the probability of rolling a number less than 1, followed by any other number, is 0/36, which simplifies to 0.
To summarize:
1. Probability of rolling a 4 then an even number: 3/36
2. Probability of rolling a 3 then a 3: 1/36
3. Probability of rolling a number less than 1 and then a number less than 2: 0/36 (which is 0)