Consider the experiment involving rolling a single die once.
What is P(even and Prime)?
I do not know how to start this can anyone help?
Which possibilities are both even and prime? Divide that by 6, the number of possibilities for a standard die.
Would they both be 1/2?
P(even and prime) means the probability of rolling a single number that is BOTH even and prime. You found P(even) and P(prime) separately.
so, because there are the same amount of even and odds wouldnt that make it a 1?
The only number that is both even and prime is 2. That is 1 possibility out of 6.
Oh.... I understand and see that now.
Of course! To find the probability of rolling a number that is both even and prime when rolling a single die, we first need to determine the total number of possible outcomes and then count the number of outcomes that satisfy the condition.
Step 1: Determine the total number of possible outcomes:
When rolling a single die, there are six possible outcomes since a die has six sides (numbers 1 to 6).
Step 2: Determine the number of outcomes that satisfy the condition:
To find the number of outcomes that are both even and prime, we need to identify the numbers on a die that fulfill both of these conditions. In this case, the only number that meets both criteria is 2, as it is the only even prime number.
Step 3: Calculate the probability:
Now that we know there is a single outcome (2) that fulfills the condition and we have six possible outcomes, we can calculate the probability by dividing the number of outcomes that satisfy the condition by the total number of possible outcomes. Thus, the probability (P) of rolling a number that is both even and prime is:
P(even and prime) = Number of outcomes that are even and prime / Total number of possible outcomes
= 1 / 6
= 1/6 ≈ 0.1667
Therefore, the probability of rolling a number that is both even and prime is approximately 0.1667 or about 16.67%.