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 P(correct)=12300P(\text{correct}) = \frac{1}{2300}.

The probability of not picking the numbers correctly is the complement of this, which is:

P(not correct)=1P(correct)=112300P(\text{not correct}) = 1 - P(\text{correct}) = 1 - \frac{1}{2300}

Let's calculate:

P(not correct)=230012300=22992300P(\text{not correct}) = \frac{2300 - 1}{2300} = \frac{2299}{2300}

Thus, the probability that you will not pick the numbers correctly is 22992300\frac{2299}{2300}, or approximately 0.99957.

Do you want more details or have any questions?

Here are 5 related questions you might find useful:

  1. What is complementary probability, and how is it used in other problems?
  2. How would the probability change if the odds were increased to 1 in 5000?
  3. Can we express this probability as a percentage?
  4. What is the probability of winning the lottery if the odds are 1 in 1 million?
  5. 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