An unbiased coin is tossed 15 times. In how many ways can the coin land tails either exactly 8 times orexactly 5 times?
1 answer:
Answer:
Probability to get tails exactly 8 times or exactly 5 times is 0.29
Step-by-step explanation:
No of ways the coins lands tails exactly 8 times
P(8) = 15C8 × ×
No of ways the coin lands tails exactly 5 times
P(5) = 15C5 × ×
Probability to get tails exactly 8 times or 5 times
P(8)+P(5) = 15C8 × + 15C5 ×
P = ( 15C8 + 15C5 )
P = ( (
) + (
) )
P = ( 6435 + 3003 )
P = ( 9438)
P = ( 4719)
P =
P = 0.29
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We will conclude that:
- The domain of the exponential function is equal to the range of the logarithmic function.
- The domain of the logarithmic function is equal to the range of the exponential function.
<h3>Comparing the domains and ranges.</h3>
Let's study the two functions.
The exponential function is given by:
f(x) = A*e^x
You can input any value of x in that function, so the domain is the set of all real numbers. And the value of x can't change the sign of the function, so, for example, if A is positive, the range will be:
y > 0.
For the logarithmic function we have:
g(x) = A*ln(x).
As you may know, only positive values can be used as arguments for the logarithmic function, while we know that:
So the range of the logarithmic function is the set of all real numbers.
<h3>So what we can conclude?</h3>- The domain of the exponential function is equal to the range of the logarithmic function.
- The domain of the logarithmic function is equal to the range of the exponential function.
If you want to learn more about domains and ranges, you can read: