Ben rolls a standard number cube (sides labeled with numbers 1 through 6). Find the probability that Ben rolls a number greater than 2 or an even number.
Events(x>2)={3,4,5,6}
Events(even)={2,4,6}
So
B=Events(x>2)∪Events(even)
={3,4,5,6}∪{2,4,6}
={2,3,4,5,6}
|B|=cardinality of B = 5
Therefore the probability is 5/6
To find the probability, we first need to determine the number of favorable outcomes (the rolls that meet the condition) and the total number of possible outcomes.
Let's start by identifying the favorable outcomes:
1. Numbers greater than 2: We have the numbers 3, 4, 5, and 6, so there are 4 favorable outcomes here.
2. Even numbers: We have 2, 4, and 6, so there are 3 favorable outcomes here.
Next, let's determine the total number of possible outcomes:
Since we have a standard number cube, it has 6 sides, and each side represents a different number from 1 through 6. Therefore, there are 6 possible outcomes.
Now that we have the number of favorable outcomes and the total number of possible outcomes, we can calculate the probability by dividing the favorable outcomes by the total number of outcomes:
Probability = (Number of Favorable Outcomes) / (Total Number of Possible Outcomes)
In this case, the probability is:
Probability = (4 + 3) / 6
Probability = 7 / 6
However, probabilities cannot exceed 1. So, in this case, we need to identify any overlapping outcomes (numbers that satisfy both conditions) and subtract their count from the favorable outcomes.
In this scenario, the overlapping numbers are 4 and 6, as they are both greater than 2 and even numbers. So, we will only count them once.
Therefore, the corrected number of favorable outcomes is 5, and the probability becomes:
Probability = 5 / 6
Hence, the probability that Ben rolls a number greater than 2 or an even number is 5/6.