The values of x and y that satisfy this system of equations are 10 and 5 respectively
<h3>Simultaneous equation</h3>Given the system of equations
x + y = 20
3x - 3y = 30
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x + y = 20
x - y = 10
Add the equations
2x = 20 + 10
2x = 30
x = 30/2
x = 15
Substitute
x -y = 10
15 - y = 10
y = 5
Hence the values of x and y that satisfy this system of equations are 10 and 5 respectively
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Answer:
<em>b. 0.6024</em>
Step-by-step explanation:
<u>Conditional Probability</u>
Suppose two events A and B are not independent, i.e. they can occur simultaneously. It means there is a space where the intersection of A and B is not empty:
If we already know event B has occurred, we can compute the probability that event A has also occurred with the conditional probability formula
Now analyze the situation presented in the question. Let's call F to the fair coin with 50%-50% probability to get heads-tails, and U to the unfair coin with 32%-68% to get heads-tails respectively.
Since the probability to pick either coin is one half each, we have
If we had picked the fair coin, the probability of getting heads is 0.5 also, so
If we had picked the unfair coin, the probability of getting heads is 0.32, so
Being A the event of choosing the fair coin, and B the event of getting heads, then
The closest answer is
b. 0.6024