Math Problem Statement
Solution
The question asks:
"A balanced die is tossed twice. Find the probability that it will show an even number in both the tosses."
Solution:
A standard balanced die has six faces with the numbers: 1, 2, 3, 4, 5, and 6. Out of these, the even numbers are: 2, 4, and 6.
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The probability of rolling an even number on a single toss is the ratio of favorable outcomes (2, 4, 6) to the total number of outcomes (1, 2, 3, 4, 5, 6):
Since the die is tossed twice, and the two events (the first toss and the second toss) are independent, the probability of getting an even number on both tosses is:
Final Answer:
The probability of rolling an even number on both tosses is .
Would you like more details on how probability works or have any questions?
Here are some related questions you might find interesting:
- What is the probability of getting an odd number on both tosses?
- How would the probability change if the die were biased?
- What is the probability of getting at least one even number in two tosses?
- How do you calculate the probability of rolling a specific number twice?
- Can you calculate the probability of getting different combinations of even and odd numbers?
Tip: In independent events, the total probability is the product of individual event probabilities.
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Math Problem Analysis
Mathematical Concepts
Probability
Independent Events
Basic Arithmetic
Formulas
P(even number) = 3/6 = 1/2
P(even on both tosses) = P(even on 1st toss) × P(even on 2nd toss)
Theorems
Multiplication Rule for Independent Events
Suitable Grade Level
Grades 7-9