Question

1. you select a card at random from the cards that make up the word

eplacement\. without replacing the card, you choose a second card. find the probability of choosing a vowel and then not a vowel. the

Explanation:

Step1: Count vowels and total letters

The word "replacement" has 11 letters. Vowels are 'e','a','e','e','a' (5 vowels).

Step2: Probability of first - card (vowel)

Probability of choosing a vowel first: \(P(V_1)=\frac{5}{11}\).

Step3: Probability of second - card (non - vowel)

After choosing a vowel, there are 10 letters left, 6 non - vowels. So \(P(NV_2|V_1)=\frac{6}{10}=\frac{3}{5}\).

Step4: Use multiplication rule for dependent events

\(P(V_1\cap NV_2)=P(V_1)\times P(NV_2|V_1)=\frac{5}{11}\times\frac{6}{10}=\frac{30}{110}=\frac{3}{11}\).

Answer:

\(\frac{3}{11}\)