Statistics and Discrete distributions

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SUMMARY

The discussion centers on calculating the probability of at least 2 individuals having blood types O or B from a sample of six random individuals, given the probabilities of blood types O (0.46), A (0.39), B (0.12), and AB (0.03). The solution involves recognizing that this scenario follows a binomial distribution, where the probability of success (having either type O or B) is 0.58. The probability can be computed using the formula P(X≥2) = 1 - P(0) - P(1), where P(0) and P(1) represent the probabilities of having 0 or 1 individual with the desired blood types, respectively.

PREREQUISITES
  • Understanding of binomial distribution
  • Basic probability concepts
  • Familiarity with probability mass functions
  • Ability to perform calculations involving combinations
NEXT STEPS
  • Learn how to calculate binomial probabilities using the binomial formula
  • Explore the concept of complementary probabilities in statistics
  • Study the application of the binomial distribution in real-world scenarios
  • Investigate the differences between binomial and Poisson distributions
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amai
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Homework Statement


The probabilities of blood types O, A, B and AB are 0.46, 0.39, 0.12, 0.03 respectively.
If a clinic is seeking either type O or B from six random individuals, what is the probability that at least 2 people have the desired blood type?

Homework Equations





The Attempt at a Solution



I'm not really sure where to start. From the questions, I don't think it's a binomial distribution or a poisson distribution. All i have so far is...

Where X=people with the desired blood type

P(X≥ 2)=1-P(0)-(P(1)

Any suggestions?
 
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Since the probability of being O is 0.46 and the probability of being B is 0.12, what is the probability of being either O or B?

What is the probability of not being either O or B, or in other words, what is the probability of being A or AB?
 
amai said:

Homework Statement


The probabilities of blood types O, A, B and AB are 0.46, 0.39, 0.12, 0.03 respectively.
If a clinic is seeking either type O or B from six random individuals, what is the probability that at least 2 people have the desired blood type?

Homework Equations





The Attempt at a Solution



I'm not really sure where to start. From the questions, I don't think it's a binomial distribution

You are conducting six independent trials, in which success in a trial is defined as "this person has type O or B blood". That gives you a binomial distribution.
 

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