A lottery game has balls numbered from 0 - 9
If a ball is selected at random, what is the probability of selecting an even numbered ball or a 5 ?
I am guessing this is Mutually exclusive event and hence used the OR= P(A)+P(B) concept
considering 0 as an even number I keep getting 1 as an answer..
help me out.. am I doing it wrong?
yes, OR=Pa + Pb
Peven=5/10 Prob5=1/10
pr OR= 6/10 or 3/5
Of course how silly of me to put 5/10 for probability of 5 -_-
To calculate the probability of selecting an even numbered ball or a 5, you are correct in using the concept of addition for mutually exclusive events.
However, it seems there might be a mistake in your calculation. Let's break it down step-by-step:
Step 1: Determine the number of favorable outcomes.
- There are 5 even numbered balls: 0, 2, 4, 6, and 8.
- There is 1 ball numbered 5.
Step 2: Determine the total number of possible outcomes.
- Since there are 10 balls numbered from 0 to 9, the total number of possible outcomes is 10.
Step 3: Calculate the probability.
- P(even) = Number of favorable outcomes / Total number of possible outcomes
- P(even) = 5 / 10 = 1/2
- P(5) = Number of favorable outcomes / Total number of possible outcomes
- P(5) = 1 / 10 = 1/10
Step 4: Combine the probabilities.
- Since the events of selecting an even numbered ball and selecting the number 5 are mutually exclusive, you can add their probabilities.
- P(even or 5) = P(even) + P(5)
- P(even or 5) = 1/2 + 1/10
- P(even or 5) = 5/10 + 1/10
- P(even or 5) = 6/10
- P(even or 5) = 3/5
Therefore, the probability of selecting an even numbered ball or a 5 is 3/5 or 0.6 (60%).
To find the probability of selecting an even numbered ball or a 5, we need to consider the total number of possible outcomes and the number of favorable outcomes.
First, let's determine the total number of possible outcomes. Since there are 10 balls numbered from 0 to 9, there are 10 possible outcomes.
Next, let's find the number of favorable outcomes, i.e., the number of even numbered balls or the number 5.
Even numbered balls: There are 5 even numbered balls (0, 2, 4, 6, and 8).
Number 5: There is only 1 ball numbered 5.
To find the number of favorable outcomes, we add the number of even numbered balls and the number 5: 5 + 1 = 6.
Now, using the formula for probability, P(A or B) = P(A) + P(B) - P(A and B), we can calculate the probability.
In this case, since the event of selecting an even numbered ball and the event of selecting the number 5 are mutually exclusive, P(A and B) is 0.
Therefore, the probability of selecting an even numbered ball or a 5 is P(A or B) = P(A) + P(B) = 6/10 = 0.6.
So, the correct probability is 0.6 or 60%.
You were correct in considering the event as mutually exclusive. However, it seems that you may have used the formula incorrectly by adding the probabilities of the individual events rather than the number of favorable outcomes.