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.
Using the volume of the rectangular prism, it is found that the three dispensers will take 1,344 in³ in Sid's refrigerator.
<h3>What is the volume of a rectangular prism?
</h3>
The volume of a rectangular prism of length l, width w and height h is given by the multiplication of these three dimensions, that is:
V = lwh.
In this problem, there are three dispensers, each with l = 4 in, h = 14 in, w = 8 in, hence the volume is given by:
V = 3 x 4 x 14 x 8 = 1,344 in³.
More can be learned about the volume of a rectangular prism at brainly.com/question/17223528
#SPJ2
130-104=26
26/130=0.2
0.2=20%
Tomas will get a 20% discount if he buys the bat.
I think that is the second one
