1/13 is the probability of choosing a letter from the word MATH then getting tails.
Step-by-step explanation:
A letter of the alphabet is chosen at a random.
The total number of alphabets = 26 letters.
Then a coin is flipped.
The total number of outcomes when a coin is flipped ⇒ Head, Tail = 2.
Now, we need to find the probability of choosing a letter from the word MATH and then getting tails.
Probability of choosing a letter from the word MATH :
P(a letter) = No.of letters in MATH / total number of alphabets.
⇒ 4/26
Probability of getting a tail when a coin is flipped :
P(a tail) = No.of tails / total outcomes.
⇒ 1/2
Probability of choosing a letter from the word MATH then getting tails :
⇒ 4/26 × 1/2
⇒ 4/52
⇒ 1/13
∴ The probability of choosing a letter from the word MATH then getting tails is 1/13.
By computing the probabilities of the individual events, we will see that the probability of choosing a letter from the word MATH then getting tails is 1/13.
When you choose a letter at random, all the letters have the same probability of being chosen.
Then the probability of randomly selecting a letter from the word MATH is just the quotient between the number of letters in that word and the total number of letters, it is:
p = 4/26
Similarly, the probability of getting tails is just 1/2.
The joint probability (of both of these events happening) is just the direct product, so we get:
P = (4/26)*(1/2) = 1/13
If you want to learn more about probabilities, you can read:
https://brainly.com/question/251701
