Two chips are draw simultaneously from an urn containing 10 chips numbered from 1 to 10. What is the probability that one of the numbers on the chips is even, and the other is odd?
there are 5 correct ones left out of 9 after first draw
so 5/9
To find the probability that one chip is even and the other is odd, we first need to determine the total number of possible outcomes.
There are 10 chips in the urn, and when two chips are drawn simultaneously, there are 10 choices for the first chip. Once the first chip is drawn, there are 9 choices for the second chip.
Therefore, the total number of possible outcomes is calculated by multiplying the number of choices for the first chip (10) by the number of choices for the second chip (9), resulting in 10 x 9 = 90 possible outcomes.
Next, let's determine the number of favorable outcomes - that is, the number of outcomes where one chip is even and the other is odd.
We have 5 even-numbered chips (2, 4, 6, 8, 10) and 5 odd-numbered chips (1, 3, 5, 7, 9).
If we consider one chip to be even and the other to be odd, there are 5 choices for the even chip and 5 choices for the odd chip.
Therefore, the number of favorable outcomes is calculated by multiplying the number of choices for the even chip (5) by the number of choices for the odd chip (5), resulting in 5 x 5 = 25 favorable outcomes.
Finally, we find the probability by dividing the number of favorable outcomes (25) by the total number of possible outcomes (90):
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 25 / 90
Probability = 5/18
Therefore, the probability that one of the numbers on the chips is even, and the other is odd is 5/18.
Well, it is 5 years since I said the answer was 5/9.
So I did it again and still get 5/9.
The only Bot who agrees with me is "Step-by-Step Bot
" Explain Bot " almost got it but must multiply by 2 because it does not matter if it is odd--even or even--odd.
I wonder why so many Bots tried to correct me 5 years later.
Well, let me tell you, probability can be quite odd sometimes. But let's calculate it together!
There are 10 chips in total, and we want to choose one even and one odd number. So, let's break it down.
First, let's calculate the probability of choosing an even number on the first draw. Out of the 10 chips, half of them are even numbers, which means 5 are even. So the probability of choosing an even number on the first draw is 5/10.
Now, after the first chip has been drawn, there are 9 chips left in the urn. We want to choose an odd number on the second draw. Out of the remaining 9 chips, half of them are odd numbers, which means 4 are odd. So the probability of choosing an odd number on the second draw is 4/9.
Finally, to find the overall probability, we just multiply the two probabilities together. (5/10) * (4/9) = 20/90 = 2/9.
So my friend, the probability of drawing one even number and one odd number simultaneously is 2/9. Remember, in the world of probability, odd things can happen!
To find the probability that one chip is even and the other chip is odd, we can consider the total number of possible outcomes and the number of favorable outcomes.
Total number of outcomes:
Since we are drawing two chips simultaneously, the total number of outcomes can be found using the formula for combinations: nCr = n! / (r!(n-r)!), where n is the total number of chips (10) and r is the number of chips drawn (2).
=> Total number of outcomes = 10C2 = 10! / (2!(10-2)!) = 45.
Favorable outcomes:
To find the number of favorable outcomes, we can calculate the possibilities for each chip.
Even number chip: There are 5 even numbers (2, 4, 6, 8, 10) in the urn.
Odd number chip: There are 5 odd numbers (1, 3, 5, 7, 9) in the urn.
Since we are drawing two chips, we can select one even number chip from the 5 even number chips in 5 different ways. For each of these selections, we can select one odd number chip from the 5 odd number chips in 5 different ways.
Therefore, the number of favorable outcomes = 5 * 5 = 25.
Probability:
The probability of selecting one even number chip and one odd number chip can be calculated by dividing the number of favorable outcomes by the total number of outcomes.
=> Probability = Favorable outcomes / Total outcomes = 25 / 45 ≈ 0.5556 or 55.56%.
So, the probability that one chip is even and the other is odd is approximately 0.5556 or 55.56%.