In a certain town, 40% of the eligible voters prefer candidate A, 10% prefer candidate B, and the remaining 50% have no preference. You randomly sample 10 eligible voters. What is the probability that 4 will prefer candidate A, 1 will prefer candidate B, and the remaining 5 will have no preference?
Answers
Answer:
Multinomial Distribution
Category:Probability
The binomial distribution allows one to compute the probability of obtaining a given number of binary outcomes.
For example, it can be used to compute the probability of getting 6 heads out of 10 coin flips.
The flip of a coin is a binary outcome because it has only two possible outcomes: heads and tails.
The multinomial distribution can be used to compute the probabilities in situations in which there are more than two possible outcomes.
For example, suppose that two chess players had played numerous games and it was determined that the probability that Player A would win is 0.40, the probability that Player B would win is 0.35, and the probability that the game would end in a draw is 0.25.
The following formula gives the probability of obtaining a specific set of outcomes when there are three possible outcomes for each event:
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p is the probability,
n is the total number of events
n1 is the number of times Outcome 1 occurs,
n2 is the number of times Outcome 2 occurs,
n3 is the number of times Outcome 3 occurs,
p1 is the probability of Outcome 1
p2 is the probability of Outcome 2, and
p3 is the probability of Outcome 3.
The formula for k outcomes is
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Note that the binomial distribution is a special case of the multinomial when k = 2.