A point $(x, y)$ with integer coordinates is randomly selected such that $0 \le x \le 8$ and $0 \le y \le 4$. what is the probab
1 answer:
Answer:
Step-by-step explanation:
A point (x, y) with integer coordinates is randomly selected such that
The possible pairs of (x,y) are:
(0,0),(0,1),(0,2),(0,3),(0,4)
(1,0),(1,1),(1,2),(1,3),(1,4)
(2,0),(2,1),(2,2),(2,3),(2,4)
(3,0),(3,1),(3,2),(3,3),(3,4)
(4,0),(4,1),(4,2),(4,3),(4,4)
(5,0),(5,1),(5,2),(5,3),(5,4)
(6,0),(6,1),(6,2),(6,3),(6,4)
(7,0),(7,1),(7,2),(7,3),(7,4)
(8,0),(8,1),(8,2),(8,3),(8,4)
The Total Possible Outcomes n(S)= 45
The pair (x, y) that satisfies the given condition (say event A: ) are:
n(A)=15
Therefore:
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Answer:
a) 76% probability that Joe is early tomorrow.
b) 64.47% conditional probability that it rained
Step-by-step explanation:
We have these following probabilities:
A 70% probability that it will rain tomorrow.
A 30% probability that it does not rain tomorrow.
If it rains, a 30% probability that Joe is late and a 100-30 = 70% probability that Joe is early.
if it does not rain, a 10% probability that Joe is late and a 100-10 = 90% probability that Joe is early.
(a) Find the probability that Joe is early tomorrow.
Either it rains(70% probability) and he is early(70% probability when it rains), or it does not rain(30% probability) and he is early(90% probability when it does not rain). So
76% probability that Joe is early tomorrow.
(b) Given that Joe was early, what is the conditional probability that it rained?
By the Bayes theorem, this probability is:
The probability that it rained and he was early divided by the probability he was early.
Rained and early
70% probability it rains.
70% probability he is early when it rains.
Early
From a), 0.76
Probability
64.47% conditional probability that it rained
Answer:
The solutions of the equation are:
4/3 and 5/8
Explanation:
To get the solution of the equation, we can either solve it algebraically or graphically.
1- algebraic solution:
The general form of the quadratic equation is:
ax² + bx + c = 0
The given equation is:
24x² - 47x + 20 = 0
By comparison, we can find that:
a = 24
b = -47
c = 20
Now, to get the roots, we will use the quadratic equation shown in the attached image.
Substituting in the equation, we would find that:
either x =
or x =
2- graphical solution:
To get the solution means to get the values of the x-intercepts.
Graphing the function (see attached image), we would find that the solutions are:
0.625 which is equivalent to 5/8
and 1.3333 which is equivalent to 4/3
Hope this helps :)
The solutions of the equation are:
4/3 and 5/8
Explanation:
To get the solution of the equation, we can either solve it algebraically or graphically.
1- algebraic solution:
The general form of the quadratic equation is:
ax² + bx + c = 0
The given equation is:
24x² - 47x + 20 = 0
By comparison, we can find that:
a = 24
b = -47
c = 20
Now, to get the roots, we will use the quadratic equation shown in the attached image.
Substituting in the equation, we would find that:
either x =
or x =
2- graphical solution:
To get the solution means to get the values of the x-intercepts.
Graphing the function (see attached image), we would find that the solutions are:
0.625 which is equivalent to 5/8
and 1.3333 which is equivalent to 4/3
Hope this helps :)