12 cards with letters in the word INDEPENDENCE are put into a bag. Two cards are randomly selected. The first card selected is not replaced. Find the probability that both card show vowels.
I counted 5 vowels in the word,
Prob(both vowels) = (5/12)(4/11) =20/132
or
prob = C(5,2) / C(12,2) = 10/66 = 5/33
Well, it looks like you've got a "wordy" problem on your hands! Let's break it down.
First, we need to know how many vowels are in the word "INDEPENDENCE." We have 'I,' 'E,' 'E,' and 'E,' so that makes a total of four vowels.
Now, we know that there are 12 cards in total, so the probability of picking one vowel card on the first pick is 4/12, which simplifies to 1/3.
Since we're not replacing the first card, we now have 11 cards remaining in the bag, with only 3 vowels left.
So, the probability of selecting a second vowel card is 3/11.
To find the probability of both events occurring, we multiply the probabilities together:
(1/3) * (3/11) = 3/33
And there you have it, the probability that both cards picked will show vowels is 3/33.
That being said, always remember, probabilities can be as tricky as a banana peel on a tightrope. So, take it with a grain of circus dust!
To find the probability that both cards show vowels,
Step 1: Count the total number of cards in the bag.
There are 12 cards in total.
Step 2: Count the number of cards with vowels.
The letters in the word "INDEPENDENCE" are: [I, N, D, E, P, N, D, E, N, C, E]
From these letters, the vowels are [I, E, E, E]
So, there are 4 cards with vowels in total.
Step 3: Find the probability.
The first card is not replaced, so once a card is chosen, it is not put back into the bag.
Since we want both cards to show vowels, the probability of choosing a vowel for the first card is 4/12.
After selecting the first vowel, there are 3 vowel cards left out of the remaining 11 cards.
Thus, the probability of selecting a vowel for the second card is 3/11.
To find the probability of both events happening, we multiply the probabilities together:
Probability = (4/12) * (3/11) = 12/132 = 1/11
Therefore, the probability that both cards show vowels is 1/11.
To find the probability that both cards show vowels, we should first determine the total number of possible outcomes and the number of favorable outcomes.
Step 1: Total number of possible outcomes
There are 12 cards in total, so the first card can be any of the 12 cards. After that, there will be 11 cards left in the bag for the second card to be selected from.
So, the total number of possible outcomes is: 12 * 11 = 132
Step 2: Number of favorable outcomes
To calculate the number of favorable outcomes, we need to determine the number of cards in the bag that are vowels. In the word "INDEPENDENCE," there are a total of 6 vowels (I, E, E, E, I, E).
When selecting the first card, the probability of choosing a vowel is 6/12 since there are 6 vowels out of 12 cards.
After the first card is chosen and not replaced, there will be 5 vowels left in the remaining 11 cards for the second card.
So, the number of favorable outcomes is: 6/12 * 5/11 = 30/132
Step 3: Calculate the probability
The probability of both cards showing vowels is the number of favorable outcomes divided by the total number of possible outcomes.
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = (30/132) / (132/132)
Probability = 30/132
Simplified, the probability is 5/22.
Therefore, the probability that both cards show vowels is 5/22.