3 years ago

What is the missing reason for line 5 in this proof?

1 answer:

5 0

Line 5 shows the division property of equality.

The division property of equality states that you can divide both sides of the equation by the same number and the equation remains the same. This equation is being divided by 4 on both sides.

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The probability of event A is x, and the probability of event B is y. If the two events are independent, which of these conditio

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If two events are independent, then

$Pr(A\cap B)=Pr(A)\cdot Pr(B)$ .

Use formulas for conditional probabilities:

$Pr(A|B)=\dfrac{Pr(A\cap B)}{Pr(B)},\\ \\ Pr(B|A)=\dfrac{Pr(A\cap B)}{Pr(A)}$ .

For independent events these formulas will be:

$Pr(A|B)=\dfrac{Pr(A\cap B)}{Pr(B)}=\dfrac{Pr(A)\cdot Pr(B)}{Pr(B)}=Pr(A),\\ \\ Pr(B|A)=\dfrac{Pr(A\cap B)}{Pr(A)}=\dfrac{Pr(A)\cdot Pr(B)}{Pr(A)}=Pr(B)$ .