the letters in the word mathematics are placed in a bag what is the probability of drawing an m replacing it then drawing another m
there are 2 m's and 11 letters.
So, each draw has a 2/11 chance of drawing an m
2 draws, so multiply 2/11 * 2/11 = 4/121
To find the probability of drawing an "m" from the word "mathematics" and then, after replacing it, drawing another "m," we need to determine the total number of letters in the word and the number of "m"s present.
Let's break it down step by step:
Step 1: Determine the total number of letters in the word "mathematics."
The word "mathematics" has 11 letters.
Step 2: Determine the number of "m"s present in the word.
The word "mathematics" has 2 "m"s.
Step 3: Calculate the probability of drawing the first "m."
The probability of drawing the first "m" is calculated as the number of "m"s (2) divided by the total number of letters (11):
Probability of drawing the first "m" = Number of "m"s / Total number of letters
= 2 / 11
Step 4: As we are replacing the first "m" back into the bag, the total number of letters remains the same, and the number of "m"s remains the same as well.
Step 5: Calculate the probability of drawing the second "m" after replacing the first one.
The probability of drawing the second "m" after replacing the first one is also 2 / 11, as the number of "m"s and the total number of letters remain the same.
Step 6: Calculate the probability of both events happening.
To find the probability of two independent events happening, we multiply their individual probabilities.
Probability of drawing an "m" and then drawing another "m" = Probability of drawing the first "m" * Probability of drawing the second "m"
= (2 / 11) * (2 / 11)
= 4 / 121
Therefore, the probability of drawing an "m," replacing it, and then drawing another "m" is 4 / 121.