You roll a number cube twice. Find the probability of the event.
Rolling a number less than 2 and then a number more than 6
Rolling an odd number then an even number
Rolling a 7 then a 5
figure the probability of each event, then just multiply them together
To find the probability of an event, we divide the number of favorable outcomes by the total number of possible outcomes.
1. Rolling a number less than 2 and then a number more than 6:
The possible outcomes for each roll of the number cube are numbers 1 through 6. There is no number less than 2 and more than 6, so the probability of this event is 0.
2. Rolling an odd number then an even number:
The possible outcomes for each roll of the number cube are numbers 1 through 6. There are three odd numbers (1, 3, 5) and three even numbers (2, 4, 6). The favorable outcomes are odd numbers first, followed by even numbers: (1,2), (1,4), (1,6), (3,2), (3,4), (3,6), (5,2), (5,4), (5,6). There are 9 favorable outcomes in total.
The total number of possible outcomes is 6 * 6 = 36 (since there are 6 possibilities for each roll).
The probability of this event is 9/36 = 1/4.
3. Rolling a 7 then a 5:
The possible outcomes for each roll of the number cube are numbers 1 through 6. There is no sum of 7 followed by a 5, so the probability of this event is 0.
To find the probability of an event, we need to know the total number of possible outcomes and the number of favorable outcomes. Let's break down each event to find the probability.
Event 1: Rolling a number less than 2 and then a number more than 6.
To find the probability of each individual roll, we can count the number of favorable outcomes and divide by the total number of possible outcomes.
- Rolling a number less than 2: There is only one favorable outcome, which is rolling a 1. The total number of possible outcomes is 6 (the numbers 1 to 6 on the number cube).
- Rolling a number more than 6: There are no favorable outcomes because the maximum number on a standard number cube is 6.
Since the second event has no favorable outcomes, the overall probability of both events occurring is 0. Therefore, the probability of rolling a number less than 2 and then a number more than 6 is 0.
Event 2: Rolling an odd number then an even number.
- Rolling an odd number: There are 3 favorable outcomes (1, 3, and 5). The total number of possible outcomes is still 6.
- Rolling an even number: There are 3 favorable outcomes (2, 4, and 6).
The probability of rolling an odd number and then an even number is found by multiplying the probabilities of both events:
(3/6) * (3/6) = 9/36 = 1/4 = 0.25
Therefore, the probability of rolling an odd number and then an even number is 0.25.
Event 3: Rolling a 7 then a 5.
- Rolling a 7: There are no favorable outcomes because the numbers on a standard number cube range from 1 to 6.
- Rolling a 5: There is only one favorable outcome, which is rolling a 5.
Since the first event has no favorable outcomes, the overall probability of both events occurring is 0. Therefore, the probability of rolling a 7 and then a 5 is 0.