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:
13y + 1
Step-by-step explanation:
8y + 5y = 13y
3 - 2 = 1
13y + 1
Answer: Yes
Step-by-step explanation: A rational number is a number that can be described as a fraction. -92 can be a fraction, therefor it's rational.
Answer:
its.....D
Step-by-step explanation:
<span>This question requests to find the inverse function of sine function. The inverse function of sine function is called arc sine. This is, the arc length whose sine is the value searched. Then you need to find the arc sin (0.6123). the result may be in radians or degrees. Only in some particular cases you can tell the arc sine without a calculator or table, it is when the sine value is a notable number (e.g. 0, 1, -1, or some others) In this case you need to use a calculator or table. With a scientific calculator make sure the mode is in degrees and then enter the number 0.6123. With that numbered entered now press the key sin^-1, which is the key for the inverse of the sine function. I did it and got 37.76 degrees. Rounded to the nearest whole degree that is 38. Then, the answer is 38 degrees. </span>
