Math Problem Statement
You choose a tile at random from a bag containing 2 A's, 2 B's, and 5 C's. You replace the first tile in the bag and then choose again. Find P(Upper C and Upper C).
Solution
To solve this problem, we are asked to find the probability of selecting two 's in a row from a bag containing:
- 2 tiles labeled
- 2 tiles labeled
- 5 tiles labeled
Step 1: Total number of tiles in the bag
The total number of tiles is:
Step 2: Probability of choosing on the first draw
The probability of drawing a on the first draw is the ratio of 's to the total number of tiles:
Step 3: Replacing the tile and drawing again
Since the tile is replaced after the first draw, the total number of tiles remains 9 for the second draw. The probability of drawing a again is:
Step 4: Calculating the probability of drawing on both draws
Since the draws are independent (the tile is replaced), the probability of drawing on both draws is the product of the individual probabilities:
Final Answer:
Would you like more details or have any questions? Here are 5 related questions you might find useful:
- What would the probability be if there were only 3 's instead of 5?
- How would the result change if there was no replacement after the first draw?
- How do probabilities change if the number of 's and 's were different?
- What is the probability of drawing at least one in two draws?
- How can the concept of replacement influence other probability problems?
Tip: When calculating probabilities with replacement, remember that the total number of outcomes remains the same between draws.
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Math Problem Analysis
Mathematical Concepts
Probability
Independent Events
Multiplication Rule for Probability
Formulas
P(A and B) = P(A) * P(B)
Theorems
Multiplication Rule for Independent Events
Suitable Grade Level
Grades 6-8