Suppose A and B are independent events. If P(A)= 0.4 and P(B) = 0.85, what is P(A and B)?
1 answer:
The value of the P(A∩B) is equal to 0.04.
We have given that,
P(A)= 0.4 and P(B) = 0.85.
We have to determine the P(A and B)
<h3>What is the formula for Independent Events?</h3>For Independent Events,
P(A) × P(B) = P(A∩B)
so we have, P(A∩B) = 0.4×0.1
P(A∩B) = 0.04
P(A') = 1 - 0.4 = 0.6
This information can be represented on a Venn diagram as shown below
P(A'∪B) means the union of everything that is not A with everything that is B
P(A'∪B) = 0.06 + 0.54 + 0.04
P(A'∪B) = 0.64
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In the given equation, as the value of <em>y</em> increase, the value of <em>x</em> also
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- Yes, 4·y = 16·x is a direct variation
Reasons:
A direct variation is a relationship that exists between two variables. It is
also known as a direct proportion which can be expressed as; y = k·x
Where <em>k</em> is a number
The given equation is 4·y = 16·x
Dividing both sides by 4 gives;
Which gives;
y = 4·x
Comparing the above equation with the equation for a direct variation gives;
y = 4·x
y = k·x
Therefore;
k = 4
The equation, y = 4·x, and therefore, the equation from which it is derived, 4·y = 16·x, is a direct variation.
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