Math Problem Statement
solve part b
Solution
Let's break down Part (b) of the question into manageable parts and solve step by step.
(i) Describe the incident in words:
The sample space grid is shown, and incident corresponds to the diagonal line where the two numbers picked are the same.
Thus, represents the event:
"The first card and second card have the same number."
(ii) Find the probability of getting :
The sample space consists of all possible outcomes when two cards are picked (with replacement). Since each card has 5 numbers (), the total sample space is:
The favorable outcomes for (same number on both cards) are:
Thus, there are 5 favorable outcomes. The probability of is:
(iii) If event is "sum of both numbers on the card is ," mark on the grid and find :
Step 1: Find outcomes where the sum
Let the numbers from the first and second cards be and , respectively. The sum includes the following pairs:
- For : →
- For : →
- For : →
Thus, the favorable outcomes are:
Step 2: Count the favorable outcomes
There are 6 outcomes where .
Step 3: Find the probability of
The probability of is:
Final Answers:
- (i) Event : "The first and second cards have the same number."
- (ii) .
- (iii) .
Would you like me to further explain any part of the solution or the steps involved? Here are 5 related questions you might find interesting:
- How do we calculate probabilities for dependent events?
- Can we visualize outcomes using other tools like tables?
- How would the probabilities change if the cards were not replaced?
- What happens if the numbers on the cards ranged from 1 to 10 instead?
- How do we define complementary probabilities for events like and ?
Tip: For problems with grids or large sample spaces, systematically count favorable outcomes to ensure accuracy.
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Math Problem Analysis
Mathematical Concepts
Probability
Sample Space
Event Analysis
Formulas
P(Event) = Number of Favorable Outcomes / Total Number of Outcomes
Addition of Numbers (Sum >= 8)
Theorems
Basic Probability Theorem
Suitable Grade Level
Grade 10-12
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