Given that events A and B are independent with p (A) = 0.25 and P (B) = 0.66, determine the value of P (B∩A)
1 answer:
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Answer:
Step-by-step explanation:
First, we need to find the common denominator
The easiest way to do this is by multiplying the two given denominators, which are 2 and 5.
2 × 5 = 10
So, our common denominator is 10. Then, multiply the numerators of the two fractions by 2 and 5. Here's why:
=
We multiplied the top and bottom by 2 to make sure our new fraction stays equivalent to the original fraction.
Do the same thing for the other one:
=
Finally, subtract the two fractions to find the difference between the two times:
=
The reason we used the common denominator is because we can only add or subtract fractions if they have the same denominator.
The answer is A: x=1/2 , y= 1/3
Solve the following system:
{2 x + 3 y = 2 | (equation 1)
{6 x + 18 y = 9 | (equation 2)
Swap equation 1 with equation 2:
{6 x + 18 y = 9 | (equation 1)
{2 x + 3 y = 2 | (equation 2)
Subtract 1/3 × (equation 1) from equation 2:
{6 x + 18 y = 9 | (equation 1)
{0 x - 3 y = -1 | (equation 2)
Divide equation 1 by 3:
{2 x + 6 y = 3 | (equation 1)
{0 x - 3 y = -1 | (equation 2)
Multiply equation 2 by -1:
{2 x + 6 y = 3 | (equation 1)
{0 x+3 y = 1 | (equation 2)
Divide equation 2 by 3:
{2 x + 6 y = 3 | (equation 1)
{0 x+y = 1/3 | (equation 2)
Subtract 6 × (equation 2) from equation 1:
{2 x+0 y = 1 | (equation 1)
v0 x+y = 1/3 | (equation 2)
Divide equation 1 by 2:
{x+0 y = 1/2 | (equation 1)
v0 x+y = 1/3 | (equation 2)
Collect results:
Answer: {x = 1/2, y = 1/3
Solve the following system:
{2 x + 3 y = 2 | (equation 1)
{6 x + 18 y = 9 | (equation 2)
Swap equation 1 with equation 2:
{6 x + 18 y = 9 | (equation 1)
{2 x + 3 y = 2 | (equation 2)
Subtract 1/3 × (equation 1) from equation 2:
{6 x + 18 y = 9 | (equation 1)
{0 x - 3 y = -1 | (equation 2)
Divide equation 1 by 3:
{2 x + 6 y = 3 | (equation 1)
{0 x - 3 y = -1 | (equation 2)
Multiply equation 2 by -1:
{2 x + 6 y = 3 | (equation 1)
{0 x+3 y = 1 | (equation 2)
Divide equation 2 by 3:
{2 x + 6 y = 3 | (equation 1)
{0 x+y = 1/3 | (equation 2)
Subtract 6 × (equation 2) from equation 1:
{2 x+0 y = 1 | (equation 1)
v0 x+y = 1/3 | (equation 2)
Divide equation 1 by 2:
{x+0 y = 1/2 | (equation 1)
v0 x+y = 1/3 | (equation 2)
Collect results:
Answer: {x = 1/2, y = 1/3