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:
540 m
Step-by-step explanation:
We are given that
Central angle,
rad
Radius of circle=18 m
We have to find the length of the arc s.
We know that
Length of arc,
Using the formula then, we get
Length of arc,
Hence, the length of arc=540 m
Since the problem gives the number of values of how far away each Eaton and Wellington are from Baxter, you can add both of the miles together to get the total distance from Eaton to Wellington.
42 1/2+37 4/5=
Find the common denominator for both of them.
42 5/10 + 37 8/10=
Answer: 80 3/10 miles from each other
Answer:
102
Step-by-step explanation:
All angles added together=180
180-13-65
180-78
102
Answer:
52
Step-by-step explanation:
f(6)= (8 × 6) + 4
= 48 + 4
= 52
