You select a card at random from the cards that make up the word “replacement”. Without replacing the card, you choose a second card. Find the probability of choosing a consonant and then an “e”. There is 1 letter for each card.
To find the probability of choosing a consonant and then an "e" without replacement, we need to calculate the probability of each event separately and then multiply them together.
First, let's determine the number of consonants in the word "replacement".
The consonants are: r, p, l, c, m, n, and t. There are 7 consonants in total.
The total number of cards in the word "replacement" is 11.
So, the probability of choosing a consonant on the first draw is 7/11.
After selecting a consonant, there are now 10 cards remaining in the word "replacement".
Now, let's determine the number of "e"s in the remaining cards.
There are 2 "e"s in the word "replacement".
Thus, the probability of choosing an "e" on the second draw, given that we already selected a consonant, is 2/10.
To find the overall probability, we multiply the probabilities of the two events:
(7/11) * (2/10) = 14/110 = 7/55
Therefore, the probability of selecting a consonant and then an "e" without replacement from the word "replacement" is 7/55.
Are you sure
Apologies for the mistake in my previous response. Let's calculate the correct probability.
In the word "replacement", there are 4 consonants: r, p, l, and c.
The total number of cards in the word "replacement" is 11.
So, the probability of choosing a consonant on the first draw is 4/11.
After selecting a consonant, there are now 10 cards remaining in the word "replacement".
Now, let's determine the number of "e"s in the remaining cards.
There are 3 "e"s in the word "replacement".
Thus, the probability of choosing an "e" on the second draw, given that we already selected a consonant, is 3/10.
To find the overall probability, we multiply the probabilities of the two events:
(4/11) * (3/10) = 12/110 = 6/55
Therefore, the correct probability of selecting a consonant and then an "e" without replacement from the word "replacement" is 6/55.
To find the probability of choosing a consonant and then an "e" from the word "replacement," we need to first determine the total number of cards with consonants and the total number of cards with "e".
Step 1: Count the number of consonants in the word "replacement":
In the word "replacement," the vowels are "a" and "e", and the letters "r", "p", "l", "c", "m", and "n" are consonants. Thus, there are 7 consonants in the word.
Step 2: Count the number of occurrences of the letter "e":
In the word "replacement," there are two "e" letters.
Step 3: Determine the total number of cards:
The total number of cards will depend on the number of letters in the word "replacement." In this case, there are 11 letters, so there are 11 cards in total.
Step 4: Calculate the probability:
To calculate the probability of choosing a consonant and then an "e," we need to consider that the card is not replaced after the first selection. The probability is calculated as the product of the probabilities of each event:
P(Consonant then "e") = (Number of consonants / Total number of cards) * (Number of "e" letters / Total number of remaining cards after the first selection)
P(Consonant then "e") = (7 / 11) * (2 / 10)
Simplifying, we get:
P(Consonant then "e") = 14 / 110
Thus, the probability of choosing a consonant and then an "e" from the word "replacement" without replacing the first card is 14/110, which can be further simplified if needed.