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# ​ A group of children were asked if they like eating cupcakes or brownies. The table shows the probabilities of the results.

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A group of children were asked if they like eating cupcakes or brownies.

The table shows the probabilities of the results.

May 16, 2018

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Here’s the math portion of the problem:

$$P(B)=0.3 \tiny \text{ Read as “The probability that a child (from the sample set) likes (B)rownies" }\\ P(C)=0.5 \tiny \text{ The probability that a child likes (C)upcakes}\\ P(B\cap C)=0.15 \tiny \text{ (The intersection of these probabilities )}\\ \\ P(B|C)=\dfrac{P(B\cap C)}{P(C)}=\dfrac{0.15}{0.5}=0.3 \tiny \text { Read as “The probability that a child likes brownies, given that s/he likes cupcakes.}\\ P(C|B)=\dfrac{P(B\cap C)}{P(B)}=\dfrac{0.15}{0.3}=0.5 \tiny \text { The probability that a child likes cupcakes, given that s/he likes brownies.}\\ \small \text {Note that }P(B|C)=P(B) \small \text { and }P(C|B)=P(C)\\$$

With this, you can logically determine which statement is true.

If you do not respond, I will not answer any more of your questions.

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GA

May 16, 2018