(a) In a certain board game, players spin a spinner to determine how many spaces they advance. The odds in favor of advancing five spaces are $$ \frac{5}{14} $$. Find the probability of advancing five spaces. (b) Tom has a box of candies with different flavors. He will randomly choose one piece of candy. The probability that he chooses a strawberry-flavored piece is $$ \frac{6}{11} $$, What are the odds against him choosing a strawberry-flavored piece? (

Question

UpStudy AI · Accepted Answer

Let's solve each part of the problem step by step.

---

### **Problem (a)**

**Given:**
- **Odds in favor** of advancing five spaces = $$ \frac{5}{14} $$.

**To Find:**
- **Probability** of advancing five spaces.

**Solution:**

1. **Understanding Odds:**
   - **Odds in favor** of an event are expressed as the ratio of the number of favorable outcomes to unfavorable outcomes.
   - If the odds in favor of an event are $$ \frac{5}{14} $$, it means for every 5 favorable outcomes, there are 14 unfavorable outcomes.

2. **Calculating Probability:**
   - **Probability** is the ratio of favorable outcomes to the total number of possible outcomes.
   - Total outcomes = Favorable outcomes + Unfavorable outcomes = $$ 5 + 14 = 19 $$.

$$
   \text{Probability} = \frac{\text{Favorable outcomes}}{\text{Total outcomes}} = \frac{5}{19}
   $$

**Answer:**
The probability of advancing five spaces is $$ \frac{5}{19} $$.

---

### **Problem (b)**

**Given:**
- **Probability** of choosing a strawberry-flavored piece = $$ \frac{6}{11} $$.

**To Find:**
- **Odds against** choosing a strawberry-flavored piece.

**Solution:**

1. **Understanding Odds Against:**
   - **Odds against** an event are expressed as the ratio of the number of unfavorable outcomes to favorable outcomes.
   - First, determine the probability of the **unfavorable** outcome (not choosing a strawberry-flavored piece).

2. **Calculating Unfavorable Probability:**
   $$
   \text{Probability of not choosing strawberry} = 1 - \frac{6}{11} = \frac{5}{11}
   $$

3. **Expressing Odds Against:**
   - The ratio of unfavourable to favourable probabilities is $$ \frac{5}{11} : \frac{6}{11} $$.
   - Simplifying the ratio by dividing both terms by $$ \frac{1}{11} $$:
     $$
     5 : 6
     $$

**Answer:**
The odds against choosing a strawberry-flavored piece are $$ 5:6 $$.

---
**Problem (a):** - Probability of advancing five spaces: $$ \frac{5}{19} $$. **Problem (b):** - Odds against choosing a strawberry-flavored piece: $$ 5:6 $$.

Real Tutor Solution

Answer

Solution

Beyond the Answer

Related Questions

Latest Probability Questions