Math Problem Statement

Number of Girls x ​P(x)

0 0.0030.003 1 0.0110.011 2 0.1060.106 3 0.2430.243 4 0.2740.274 5 0.2430.243 6 0.1060.106 7 0.0110.011 8 0.0030.003

Find the probability of getting exactly 6 girls in 8 births.

Solution

To find the probability of getting exactly 6 girls in 8 births, you can simply use the probability distribution provided.

From the table:

  • The number of girls x=6x = 6
  • The corresponding probability P(x=6)=0.106P(x = 6) = 0.106

Thus, the probability of getting exactly 6 girls in 8 births is 0.1060.106 or 10.6%.

Would you like more details on how this is part of a binomial distribution or any other clarification?

Here are 5 related questions to expand on this:

  1. What is the total probability of all possible outcomes (0 to 8 girls)?
  2. How do you calculate the expected number of girls in 8 births?
  3. What is the probability of getting at least 5 girls in 8 births?
  4. How would you calculate the probability of getting fewer than 3 girls in 8 births?
  5. What is the variance and standard deviation for the number of girls in 8 births?

Tip: When analyzing probability distributions, always ensure that the sum of probabilities for all possible outcomes equals 1. This helps confirm the validity of the distribution.

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Math Problem Analysis

Mathematical Concepts

Probability
Binomial Distribution

Formulas

P(x = k) for binomial distribution = (n choose k) * p^k * (1-p)^(n-k)
Sum of probabilities = 1

Theorems

Binomial Theorem
Law of Total Probability

Suitable Grade Level

Grades 9-12