You write each letter of the word MATHEMATICIAN on a piece of paper and put each letter in a bag. You randomly select one piece from the bag. What is P(T or A)?
P(T or A) = P(T) + P(A) - P(T and A)
To find P(T), we count the number of T's in MATHEMATICIAN, which is 2. So, P(T) = 2/12 = 1/6.
To find P(A), we count the number of A's in MATHEMATICIAN, which is also 2. So, P(A) = 2/12 = 1/6.
To find P(T and A), we count the number of letters that are both T and A, which is 0.
Therefore, P(T or A) = 1/6 + 1/6 - 0 = 1/3.
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To calculate the probability of selecting either the letter T or the letter A from the bag, we need to first determine the total number of letters in the word MATHEMATICIAN and then count how many of those letters are T or A.
Step 1: Count the total number of letters in the word MATHEMATICIAN.
In this case, the word has 13 letters.
Step 2: Count how many of the letters are T or A.
There are 2 letters in the word MATHEMATICIAN that are either T or A, which are the letters T and A themselves.
Step 3: Calculate the probability of selecting either T or A.
The probability is determined by dividing the number of desired outcomes (in this case, either T or A) by the total number of possible outcomes (the total number of letters in the word).
P(T or A) = (Number of T or A) / (Total number of letters)
P(T or A) = 2 / 13
Therefore, the probability of randomly selecting either the letter T or the letter A from the bag is 2/13.