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
- The corresponding probability
Thus, the probability of getting exactly 6 girls in 8 births is 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:
- What is the total probability of all possible outcomes (0 to 8 girls)?
- How do you calculate the expected number of girls in 8 births?
- What is the probability of getting at least 5 girls in 8 births?
- How would you calculate the probability of getting fewer than 3 girls in 8 births?
- 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