farzad puts the following 11 cards into a bag...
farzad puts the following 11 cards into a bag: a s s e s s m e n t. farzad randomly selects one card, records the result and puts the card back into the bag. if he does this 500 times, how many times is it likely that he will select a card with a vowel (a, e, i, o, u)? justify your answer.
Answer
# Explanation:
## Step1: Count total letters and vowels
The word "ASSESSMENT" has 10 letters. The vowels in it are 'A', 'E', 'E', 'E' so there are 4 vowels.
## Step2: Calculate probability of selecting a vowel
The probability $P$ of selecting a vowel in one - draw is the number of vowels divided by the total number of letters. So $P=\frac{4}{10}=\frac{2}{5}$.
## Step3: Use probability to predict number of vowel - selections in 500 draws
If the experiment is repeated 500 times, the expected number of times a vowel is selected is the probability of selecting a vowel times the number of trials. Let $n$ be the number of times a vowel is selected. Then $n = P\times500$. Substituting $P=\frac{2}{5}$ into the formula, we get $n=\frac{2}{5}\times500 = 200$.
# Answer:
200