Question
At a beach, the probability of having high waves on any given day is 0.22 . 3. What is the probability of having high waves on three consecutive days at this beach? A. 0.0106 B. 0.0206 C. 0.0484 D. 0.4746
Ask by Mcguire Love. in Egypt
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The probability of having high waves on three consecutive days is 0.0106.
Solution
To determine the probability of having high waves on three consecutive days at the beach, we'll assume that the events are independent. This means the probability of high waves on each day does not affect the probability on any other day.
Given:
- Probability of high waves on any given day, \( P = 0.22 \)
The probability of having high waves on three consecutive days is calculated by multiplying the probability for each day:
\[
P(\text{3 consecutive days}) = P \times P \times P = 0.22 \times 0.22 \times 0.22
\]
Let's compute this step by step:
1. First, calculate \( 0.22 \times 0.22 \):
\[
0.22 \times 0.22 = 0.0484
\]
2. Next, multiply the result by \( 0.22 \):
\[
0.0484 \times 0.22 = 0.010648
\]
Rounding to four decimal places gives \( 0.0106 \).
**Answer:**
A. 0.0106
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Simplify this solution The Deep Dive
To find the probability of having high waves on three consecutive days, we can multiply the probability of high waves on a single day by itself for three days: \[ P(\text{3 consecutive days}) = P(\text{high waves})^3 = 0.22^3 = 0.010648. \] So, rounding it gives us approximately 0.0106. The correct answer is **A. 0.0106**. For future reference, when dealing with probabilities over multiple independent events, be sure to multiply the probabilities together. It’s a crucial skill for all types of probability puzzles or real-life applications like weather forecasting! Always check if events are indeed independent before applying this rule.
