Smith has '4' bats namely B1, B2, B3, B4. He randomly selects
one out of the three bats which was not used in the previous match. If
for his first match the chosen bat was B1 and what is the probability
that he uses B1 again in the 6th Match? (3 attempts) We checked answer 4/27 and 1/3 bothare wrong .should we use bayes theorem.this is our last chance .kindly give the correct and accurate answer

To solve this problem correctly, we need to consider the way the selection process works, and account for the rules that dictate how bats are chosen over multiple matches.

### Given:
- Smith has 4 bats: B1, B2, B3, B4.
- For the first match, Smith uses B1.
- In every subsequent match, he selects one of the three bats that were **not** used in the previous match.
- We want to determine the probability that Smith uses B1 again in the 6th match.

### Solution Approach:
Since Smith is selecting one of the three bats that were not used in the previous match, each bat (excluding the previously used one) has an equal probability of being chosen.

#### Let's break down the matches:

1. **1st Match:** B1 is used.
2. **2nd Match:** Smith can choose any of B2, B3, or B4 (since B1 was used in the 1st match). Each bat has a probability of \( \frac{1}{3} \).
3. **3rd Match:** Smith can now choose any of the three bats **not used in the 2nd match**. Again, each bat has a \( \frac{1}{3} \) probability.
4. **4th Match:** The bat used here must be one of the three not used in the 3rd match. Again, each has a \( \frac{1}{3} \) probability.
5. **5th Match:** Smith will choose one of the three bats not used in the 4th match.
6. **6th Match:** Smith will choose one of the three bats not used in the 5th match.

### Key Point:
For Smith to use B1 in the 6th match, B1 must be one of the three

Explore the probability problem where Smith selects bats randomly for matches, considering rules for not reusing bats consecutively. Calculate the probability of using B1 again in the 6th match using Bayes' Theorem and sequential selection rules.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation