Answer:
(a)
The probability that you stop at the fifth flip would be

(b)
The expected numbers of flips needed would be

Therefore, suppose that
, then the expected number of flips needed would be 1/0.5 = 2.
Step-by-step explanation:
(a)
Case 1
Imagine that you throw your coin and you get only heads, then you would stop when you get the first tail. So the probability that you stop at the fifth flip would be

Case 2
Imagine that you throw your coin and you get only tails, then you would stop when you get the first head. So the probability that you stop at the fifth flip would be

Therefore the probability that you stop at the fifth flip would be

(b)
The expected numbers of flips needed would be

Therefore, suppose that
, then the expected number of flips needed would be 1/0.5 = 2.
A, C, And D
Could be these answers...
Answer:
the critical points are (0,0) , (0, 20), (12, 0) , (4,16)
Step-by-step explanation:
To consider the autonomous system


The critical points of the above system can be derived by replacing x' = o and y' = 0.
i.e.


x = 0 or 24 - 2x - y = 0 ----- (1)
Also

y( 20 -y - x) = 0
y = 0 or 20 - y - x = 0 ----- (2)
By solving (1) and (2);
we get x = 4 and y = 16
Suppose x = 0 from (2)
y = 20
Also;
if y = 0 from (1)
x = 12
Thus, the critical points are (0,0) , (0, 20), (12, 0) , (4,16)
Answer:
Probability that she or he bought lunch in the cafeteria and chose pizza as an entree = 12/100 =0.12 = 12%
Explanation:
Let number of students be 100.
At Taylor Street School, 40% of the students bought lunch in the cafeteria today
Number of students bought lunch = 100 x 40/100 = 40
Of the students who bought lunch in the cafeteria today, 30% chose pizza as their entree
Number of students bought pizza = 40 x 30/100 = 12.
Probability of an outcome = Number of favorable outcome/ Total number of outcome
Probability that she or he bought lunch in the cafeteria and chose pizza as an entree = Number of students bought pizza/Total number of students
= 12/100 =0.12 = 12%
Probability that she or he bought lunch in the cafeteria and chose pizza as an entree = 12/100 =0.12 = 12%
Here is the work for this equation:
2+9-x/4 =10
11-x/4=10
11-x=40
x=29