A letter of the alphabet is chosen at a random ,then a coin is flipped. What is the probability of choosing a letter from the word MATH then getting tails

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

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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.

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step-by-step explanation: