Consider the experiment of rolling a single die. Find the probability of the event described. What is P(odd or prime?
Since this is an "or" problem would the problem consist of 3 chances out of 6 thus my answer = 1/2?
the odd numbers on a die are 1,3,5
the prime numbers on a die are 2,3,5
(2 is the first prime number and the only even one)
so there are 4 numbers that you are interested in
prob(odd or prime) = 4/6 = 2/3
To find the probability of the event "odd or prime" when rolling a single die, we need to determine the number of favorable outcomes (outcomes that satisfy the condition) and divide it by the total number of possible outcomes.
First, let's find the number of odd numbers on a die. A die has 6 sides, and 3 of those sides have odd numbers (1, 3, 5).
Next, let's determine the number of prime numbers on a die. The prime numbers between 1 and 6 are 2, 3, and 5. Thus, there are 3 prime numbers on a die.
Now, we need to account for the fact that the number 3 is both odd and prime. We don't want to count it twice, so we need to subtract it once from the total count. Therefore, the total number of outcomes satisfying "odd or prime" is 3 + 2 - 1 = 4.
Finally, since a die has 6 equally likely outcomes (numbers 1 to 6), the probability of the event "odd or prime" is given by the number of favorable outcomes (4) divided by the total number of outcomes (6):
P(odd or prime) = 4/6 = 2/3
So, the correct answer is 2/3, not 1/2.