Using a Venn diagram to understand the multiplication rule for probability a

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Bellevue College *

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Statistics

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May 13, 2024

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2/24/24, 9:22 AM ALEKS Student Name : Denise Widell Date: 02/24/2024 9:01 AM % ALE Ks@ Login Name : DWIDELL/ Class Name : Pre-Statistics © Probability Using a Venn diagram to understand the multiplication rule for probability e SAMPLE QUESTION The Venn diagram below shows the 9 students in Ms. Coleman's class. The diagram shows the memberships for the Chess Club and the Science Club. A student from the class is randomly selected. Let 4 denote the event "the student is in the Chess Club.” Let B denote the event "the student is in the Science Club." The outcomes for the event A4 are listed in the circle on the left. The outcomes for the event B are listed in the circle on the right. Note that Yolanda is outside the circles since she is not a member of either club. Chess Science Chang Jessica Rafael Keith Teresa Yolanda (a) Find the probabilities of the events below. Write each answer as a single fraction. P(A4) = P(B) = P(AandB) = P(4|B) = P(B)-P(4|B) = (b) Select the probability that is equal to P(A4 and B). O P(4|B) O P(B) O P(4) O P(B)-P(4|B) @ EXPLANATION (a) We are asked to find the probabilities of several events. https://www-awa.aleks.com/alekscgi/x/Isl.exe/15NeYKrL8KKkbJsgusCiSGhYaV7MNK krc45XMR499GOW1AG6LjE9kURWowyj98Hg3DdOhuQStI9j0Q... 1/4
2/24/24, 9:22 AM A student from the class is randomly selected. ALEKS There are 9 students in all, and each student is equally likely to be selected. Finding P (A4): The event 4 is the event that the student is in the Chess Club. Note that an outcome for this event is a student listed in the circle on the left. The number of students (outcomes) displayed in the shaded region is 7. To find the probability of the event A, we divide the number of students in the shaded region by the total number of students. P(A)=% Finding P(B): The event B is the event that the student is in the Science Club. Note that an outcome for this event is a student listed in the circle on the right. The number of students (outcomes) displayed in the shaded region is 3. To find the probability of the event B, we divide the number of students in the shaded region by the total number of students. 3 1 P(B)—g—g Finding P(A4 and B): The event "4 and B" is the event that the student is in the Chess Club and the Science Club. The outcomes for this event are listed in the region shared by the two circles. The number of students who are members of both clubs is 2. To find the probability of the event "4 and B", we divide the number of students in the shaded region by the total number of students. 2 P(A4 and B) = 9 Finding P (A4 | B): Yolanda Chess Science Chang Jessica Rafael Keith Teresa Yolanda Chess Science Chang Jessica Rafael Keith Teresa Yolanda Chess Science Chang Jessica Rafael Keith Teresa https://www-awa.aleks.com/alekscgi/x/Isl.exe/15NeYKrL8KKkbJsgusCiSGhYaV7MNK krc45XMR499GOW1AG6LjE9kURWowyj98Hg3DdOhuQStI9j0Q... 2/4
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