use for questions 4 - 6: a letter is randomly chosen from the word candlestick. find each probability. 4…

Explanation:

Step1: Count total letters

The word "CANDLESTICK" has 11 letters. So the total number of possible outcomes is 11.

Step2: Find vowels for 4

The vowels in the word are 'A', 'E', 'I'. There are 3 vowels. So $P(\text{a vowel})=\frac{3}{11}$.

Step3: Find number of 'N' and 'S' for 5

There is 1 'N' and 1 'S' in the word. Using the addition - rule for mutually - exclusive events $P(N\text{ or }S)=P(N)+P(S)$. Since $P(N)=\frac{1}{11}$ and $P(S)=\frac{1}{11}$, then $P(N\text{ or }S)=\frac{1 + 1}{11}=\frac{2}{11}$.

Step4: Find number of 'C' for 6

There are 2 'C's in the word. So $P(C)=\frac{2}{11}$. Then, using the complement rule $P(\text{not }C)=1 - P(C)=1-\frac{2}{11}=\frac{11 - 2}{11}=\frac{9}{11}$.

Answer:

4. $\frac{3}{11}$
5. $\frac{2}{11}$
6. $\frac{9}{11}$