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nata0808 [166]
3 years ago
13

Explain why P(A|D) and P(D|A) from the table below are not equal.

Mathematics
2 answers:
Archy [21]3 years ago
6 0

Answer:

Sample Response: The two conditional probabilities are not equal because each has different given events. P(A|D) has event D as its given event, resulting in 2/10 for a probability. P(D|A) has event A as its given event, resulting in 2/8 for a probability.

trasher [3.6K]3 years ago
5 0

Answer:

The Probability that Event A and  Event D occur is equal to the probability Event A occurs times the probability that Event D occurs, given that A has occurred.


P(A\cap D)=P(A)\cdot P(D/A)

We can find the values of P(A/D) and P(D/A) using the above form formula.

P(D/A)=\frac{P(A\cap D)}{P(A)} ;

P(A/D)=\frac{P(D\cap A)}{P(D)}

From the given table, we have the values of P(A), P(D), P(D\cap A) and P(A\cap D).

Since, Probability=\frac{The number of wanted outcomes }{the number of possible outcomes}

∴P(A)=\frac{8}{17}, P(D)=\frac{10}{17}, P(A\cap D)=\frac{2}{17} and P(D\cap A)=\frac{2}{17}

Now, putting these values in above formula we get,

P(D/A)=\frac{\frac{2}{17}} {\frac{8}{17}}

P(D/A)=\frac{2} {8}=\frac{1}{4}

P(D/A)= \frac{1}{4}.

P(A/D)=\frac{\frac{2}{17}} {\frac{10}{17}}=\frac{2}{10}

P(A/D)=\frac{1}{5}

As, you can see above that the values of P(A|D) and P(D|A) are not equal.









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