Represent and Determine Probability Question
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Grade 10 Represent and Determine Probability CCSS: HSS-CP.A.3
Mary is doing an experiment where she chooses two marbles, one after the other without replacement, from a bag of marbles. The bag of consists of 5 green, 6 red, and 9 blue marbles. She wants to find the probability that she chooses a blue marble given that she chose a green marble first. She lets G be the event that she chooses a green marble and B be the event that she chooses a blue marble. Mary reasons that, since P(G)=14 and P(B)=920, P(G then B)=980. (She uses "then" instead of "and" because the events happen one after the other). Therefore, she determines that P(B∣G)=920. Is she correct, and why?
- Yes, her assumptions and steps are all correct.
- No, she assumed that G and B are independent when they are not. P(G then B)=976, and therefore P(B∣G)=919.
- No, she calculated P(G then B) incorrectly. P(G then B)=1420=710, and therefore P(B∣G)=145.
- No, she found P(G then B), when this is unnecessary. Since the events are independent, she can simply say P(G)=P(G∣B).