5. Binomial Distribution & Discrete Random Variables
Hypergeometric Distribution
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A school is holding a fair raffle and a teacher is interested in predicting how many winners will be from her class. Determine which probability distribution she should use given the following information.
(A) There are 386 tickets, one for each student. Tickets are placed back in the pool after being chosen and 5 tickets are drawn.
A
Binomial
B
Hypergeometric
Verified step by step guidance1
Step 1: Begin by analyzing the problem. The teacher wants to predict the number of winners from her class. This involves counting the number of successes (winners) in a fixed number of trials (ticket draws).
Step 2: Consider the key characteristics of the situation. There are 386 tickets, and each ticket represents a student. After a ticket is drawn, it is placed back into the pool, meaning the probability of success remains constant for each draw.
Step 3: Recall the properties of the Binomial distribution. It is used when there are a fixed number of trials, each trial is independent, and the probability of success remains constant. Since tickets are replaced after being drawn, this situation fits the Binomial distribution.
Step 4: Contrast this with the Hypergeometric distribution. The Hypergeometric distribution is used when trials are dependent, meaning the probability of success changes after each draw. This would apply if tickets were not replaced, but in this case, tickets are replaced, so the Hypergeometric distribution is not appropriate.
Step 5: Conclude that the teacher should use the Binomial distribution to model the number of winners from her class, as the conditions align with its properties.
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