Answer:
Step-by-step explanation:
In other words, carl's losing odds are 7 : 5, so his winning odds will be 5 : 7
So if they play (7+5=12) 12 times, carl will win 5 times.
To find probability that carl will beat his friend, we take the probability of Carl winning. Simple!
The probability is 5/ 12
To answer this, set up a system of equations. What we know is that
5x + 2y = 100
And...
x+y=38
x represents the unknown number of 5 points questions
y represents the unknown number of 2 point questions
In my opinion the easiest way to solve this is to use substitution (that is when you find out the value of one variable, either x or y, and substitute that value as the variable).
So,
x+y=38
Subtract x from both sides
y=38-x
Now, plug (38-x) in as y in the other equation.
5x + 2(38-x) = 100
5x + 76-2x= 100
3x+76=100
3x=24
x=8
Now that you know that x=8, you can solve for y.
5x+2y=100
5(8)+2y=100
40+2y=100
2y=60
---- ------
2 2
y=30
X=8
Y=30
There are 8 five point questions on the test and 30 two point questions on the test
Answer
well sorry cant answer the other question see if it works on here
Step-by-step explanation:
The probability that after re-rolling these three dice, at least three of the five dice show the same value is 
Of the three dice rolled, one may match the original pair and two are different, and this can occur three ways:
[ where 
is the probability of matching the first two and 
is the probability of not matching the first two ]
Or, two may match the original pair and one is different
Or, all three may match the original pair
Or, all three may be the same, but not match the original pair:
[ where is the probability of getting a new number and is the probability of matching that new number ]
Adding these together: 
To learn more about probability with the given link
brainly.com/question/11234923
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