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.
(B) There are 386 tickets, one for each student. Tickets are removed from the pool after being chosen and 5 tickets are drawn.
A
Binomial
B
Hypergeometric
Verified step by step guidance1
Step 1: Understand the problem setup. The teacher wants to predict the number of winners from her class. There are 386 tickets in total, and 5 tickets are drawn without replacement. This means the probability of selecting a ticket changes after each draw.
Step 2: Recall the key difference between the Binomial and Hypergeometric distributions. The Binomial distribution assumes that each trial is independent (e.g., drawing with replacement), while the Hypergeometric distribution is used when trials are dependent (e.g., drawing without replacement).
Step 3: Identify the characteristics of the problem. Since tickets are removed from the pool after being chosen, the draws are dependent, which aligns with the Hypergeometric distribution.
Step 4: Define the parameters of the Hypergeometric distribution. The distribution is characterized by three parameters: the population size (N = 386), the number of successes in the population (k, which would be the number of tickets belonging to the teacher's class), and the number of draws (n = 5).
Step 5: Conclude that the Hypergeometric distribution is the appropriate choice for this problem because the draws are dependent, and the probability of selecting a ticket changes after each draw.
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