Answer:
A darts player practices throwing a dart at the bull’s eye on a dart board. Her probability of hitting the bull’s eye for each throw is 0.2.
(a) Find the probability that she is successful for the first time on the third throw:
The number F of unsuccessful throws till the first bull’s eye follows a geometric
distribution with probability of success q = 0.2 and probability of failure p = 0.8.
If the first bull’s eye is on the third throw, there must be two failures:
P(F = 2) = p
2
q = (0.8)2
(0.2) = 0.128.
(b) Find the probability that she will have at least three failures before her first
success.
We want the probability of F ≥ 3. This can be found in two ways:
P(F ≥ 3) = P(F = 3) + P(F = 4) + P(F = 5) + P(F = 6) + . . .
= p
3
q + p
4
q + p
5
q + p
6
q + . . . (geometric series with ratio p)
=
p
3
q
1 − p
=
(0.8)3
(0.2)
1 − 0.8
= (0.8)3 = 0.512.
Alternatively,
P(F ≥ 3) = 1 − (P(F = 0) + P(F = 1) + P(F = 2))
= 1 − (q + pq + p
2
q)
= 1 − (0.2)(1 + 0.8 + (0.8)2
)
= 1 − 0.488 = 0.512.
(c) How many throws on average will fail before she hits bull’s eye?
Since p = 0.8 and q = 0.2, the expected number of failures before the first success
is
E[F] = p
q
=
0.8
0.2
= 4.
Answer:
3
Step-by-step explanation:
Evaluate the limit n - > ∞ 12n^3 - 2n^2 + 9 / 4n^3
Divide the expression by the highest power of n to have
limit n - > ∞ 12n³/n³ - 2n²/n³ + 9/n³ / 4n³/n³
= limit n - > ∞12 - 2/n + 9/n³ / 4
Substitute the value of n
= 12 - 2/∞ + 9/∞³ / 4
Since a/∞ = 0
The expression becomes;
= 12 - 0+ 0/4
= 12/4
= 3
Hence the required limit is 3
Answer:
f(x) = 2+5
g(x) = 2(-(x−3))+5
Step-by-step explanation:
If you remember, an absolute value can have two different answer, a positive and negative answer because the absolute value symbol makes all values in it positive. Example: |-2|=2 and |2|=2
So if y = 2|x−3|+5
then the two possibilities are
y = 2(x−3)+5 and
y = 2(-)+5
Set one of them equal to f(x) and the other one to g(x)
f(x) = 2(x−3)+5
g(x) = 2(-(x−3))+5
You can also write it as a piecewise function.
Answer:
Step-by-step explanation:
We are given that a segment FH and G is the midpoint of FH.
FH=
We have to find the measure of FH.
When G is the midpoint of segment FH
Then , FG=GH
Segment addition property
Substitution property
Substitute the values then we get
Answer:
108
Step-by-step explanation:
The exterior angle is equal to the sum of the opposite interior angles
<1 + <2 = <4
33 + 75 = <4
108 = <4
