Math Problem Statement

Find the probability of getting 6 or more girls in 8 births.

Solution

To find the probability of getting 6 or more girls in 8 births, we need to sum the probabilities from the distribution for x6x \geq 6.

From the table:

  • P(6)=0.115P(6) = 0.115
  • P(7)=0.026P(7) = 0.026
  • P(8)=0.001P(8) = 0.001

The probability of getting 6 or more girls is:

P(X6)=P(6)+P(7)+P(8)P(X \geq 6) = P(6) + P(7) + P(8)

Substituting the values:

P(X6)=0.115+0.026+0.001=0.142P(X \geq 6) = 0.115 + 0.026 + 0.001 = 0.142

So, the probability of getting 6 or more girls in 8 births is 0.142.

Would you like more details or have any questions?

Related Questions:

  1. What is the probability of getting exactly 5 girls in 8 births?
  2. How do we calculate the expected number of girls in 8 births from this distribution?
  3. What is the variance of the number of girls in 8 births?
  4. How would the probability change if the total number of births were different?
  5. Can we determine if the distribution follows a binomial pattern?

Tip:

When working with probability distributions, always ensure the sum of all probabilities equals 1 to validate the distribution's correctness.

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Math Problem Analysis

Mathematical Concepts

Probability
Binomial Distribution

Formulas

Binomial Probability Formula

Theorems

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Suitable Grade Level

High School