a coin is tossed, then a letter from the word incredible is chosen at random. what is the probability of…

Explanation:

Step1: Calculate probability of coin - toss and letter - selection separately

The probability of getting heads when tossing a fair coin is $P(H)=\frac{1}{2}$. The word "INCREDIBLE" has 10 letters, and the vowels in it are 'I', 'E', 'I', 'I', 'E', so there are 5 vowels. The probability of choosing a vowel from the word "INCREDIBLE" is $P(V)=\frac{5}{10}=\frac{1}{2}$.

Step2: Use the multiplication rule for independent events

Since the coin - toss and the letter - selection are independent events, the probability of both events occurring is the product of their individual probabilities. So $P = P(H)\times P(V)$. Substitute $P(H)=\frac{1}{2}$ and $P(V)=\frac{1}{2}$ into the formula: $P=\frac{1}{2}\times\frac{1}{2}=\frac{1}{4}$.

Answer:

$\frac{1}{4}$