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DEVELOPING EXPERT VOICES Applied Math 40s 2007 CREATOR: JENNIFER Question 3 : Probability

PROBABILITY: Question 1 List all the possibilities of the girls or boys that they might have using a sample space and a tree diagram. What is the probability that Suzy and Bret will have at least 3 girls? What is the probability that they will have exactly 2 boys? Suzy and Brian decide to start a family. They plan to have 4 kids. Answer the following questions:

PROBABILITY: Answer – Q.3 Part A List all the possibilities of the girls or boys that they might have using a sample space and a tree diagram. When asked for a sample space, all that you need to do is write down all the possible outcomes, but be careful not to miss any possibilities! SAMPLE SAPCE BBBB BBBG BBGB BBGG BGBB BGBG BGGB BGGG GBBB GBBG GBGB GBGG GGBB GGBG GGGB GGGG

PROBABILITY: Answer – Q.3 Part A List all the possibilities of the girls or boys that they might have using a sample space and a tree diagram. You could also answer your question with a tree diagram. Doing the question this way, you can be sure that you found ALL the possibilities! Since a mother giving birth to a baby is a 50/50 chance, the tree diagram will start off with 2 braches, one representing 50% of giving birth to a boy, and the other representing 50% giving birth to a girl. This branch represents the sex of the first child. The sex of the second is determined by the next set of branches. Again, there are 2 branches coming out from the first child because there is a 50/50 chance of having another boy or girl. Repeat this 2 more times...

PROBABILITY: Answer – Q.3 Part A … until you end up with this diagram The tree diagram gives you the same answers as the sample space. And each time there is 50% of giving birth to a boy, and 50% of giving birth to a girl. BBBB BBB G BB G B BB GG B G BB B G B G B GG B B GGG G BBB G BB G G B G B G B GG GG BB GG B G GGG B GGGG There is a total of 16 possibilities of giving birth to a girl or boy, when trying to have 4 children.

PROBABILITY: Answer – Q.3 Part B b) What is the probability that Suzy and Bret will have at least 3 girls? By looking at all the possibilities, there are 5 successes where they will have at least 3 girls. P( at least 3 girls) = 5/16 or 31.25%

PROBABILITY: Answer – Q.3 Part C c) What is the probability that they will have exactly 2 boys? By looking at all the possibilities, there are 6successes where they will have exactly 2 boys. P( exactly 2 boys) = 6/16 or 37.5%

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