Math Problem Statement
If there is a 1 in 2300 chance that you will pick the numbers correctly in tonight's lottery, what is the probability that you will not pick the numbers correctly?
Solution
To calculate the probability that you will not pick the numbers correctly, we can use the concept of complementary probability.
Given:
- The probability of picking the numbers correctly is .
The probability of not picking the numbers correctly is the complement of this, which is:
Let's calculate:
Thus, the probability that you will not pick the numbers correctly is , or approximately 0.99957.
Do you want more details or have any questions?
Here are 5 related questions you might find useful:
- What is complementary probability, and how is it used in other problems?
- How would the probability change if the odds were increased to 1 in 5000?
- Can we express this probability as a percentage?
- What is the probability of winning the lottery if the odds are 1 in 1 million?
- How would you calculate the probability of winning two lotteries back-to-back?
Tip: The sum of the probabilities of an event and its complement is always equal to 1.
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Math Problem Analysis
Mathematical Concepts
Probability
Complementary Probability
Formulas
P(not correct) = 1 - P(correct)
P(correct) = 1 / 2300
Theorems
Complement Rule of Probability
Suitable Grade Level
Grades 9-10
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