Advanced Placement (AP), 03.02.2021 17:00 pearl264

Mason never has a pencil when test day rolls around. Because the classmates are tired of having to supply pencils for Mason, only 15% of students will give Mason a pencil when asked. Today is test day and Mason begins asking randomly selected students for a pencil. Let Y = the number of students Mason asks until he finds someone who will give him a pencil. Describe this probability distribution. Be sure to check the appropriate conditions.

What is the probability that the third person asked is the first person who gives him a pencil?

What is the probability that Mason gets a pencil by the third person he would ask?

How many people should Mason expect to ask before getting a pencil?

Should Mason be surprised if Mason didn’t receive a pencil until he asked at least 10 people? Calculate a probability to justify your answer.

Find the standard deviation for the distribution of the number of people he asks for a pencil before finding someone who will give him one.

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