MATHEMATICS HIGH SCHOOL

You are at a stall at a fair where you have to throw a ball at a target. There are two versions of the game. In the firstversion, you are given three attempts, and you estimate that your probability of success on any given throw is 0.1.
In the second version, you are given five attempts, but the target is smaller, and you estimate that your probability of
success on any given throw is 0.05. The prizes for the two versions of the game are the same, and you are willing to
assume that the outcomes of your throws are independent. Which version of the game should you choose? (Hint: In
the first version of the game, the probability that you do not get the prize is the probability that you fail on all three
attempts.)

Answers

Answer 1

Answer:

Answer:

$P(X=0)=(3C0)(0.1)^0 (1-0.1)^(3-0)=0.729$

And the probability of loss with the first wersion is 0.729

$P(Y=0)=(5C0)(0.05)^0 (1-0.05)^(5-0)=0.774$

And the probability of loss with the first wersion is 0.774

As we can see the best alternative is the first version since the probability of loss is lower than the probability of loss on version 2.

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Solution to the problem

Alternative 1

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=3, p=0.1)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^(n-x)$

Where (nCx) means combinatory and it's given by this formula:

$nCx=(n!)/((n-x)! x!)$

We can find the probability of loss like this P(X=0) and if we find this probability we got this:

$P(X=0)=(3C0)(0.1)^0 (1-0.1)^(3-0)=0.729$

And the probability of loss with the first wersion is 0.729

Alternative 2

Let Y the random variable of interest, on this case we now that:

$Y \sim Binom(n=5, p=0.05)$

The probability mass function for the Binomial distribution is given as:

$P(Y)=(nCy)(p)^y (1-p)^(n-y)$

Where (nCx) means combinatory and it's given by this formula:

$nCy=(n!)/((n-y)! y!)$

We can find the probability of loss like this P(Y=0) and if we find this probability we got this:

$P(Y=0)=(5C0)(0.05)^0 (1-0.05)^(5-0)=0.774$

And the probability of loss with the first wersion is 0.774

As we can see the best alternative is the first version since the probability of loss is lower than the probability of loss on version 2.

Related Questions

Plz help fast Question 1(Multiple Choice Worth 5 points) (8.01 LC) Two lines, A and B, are represented by the equations given below: Line A: x + y = 6 Line B: x + y = 4 Which statement is true about the solution to the set of equations? There are infinitely many solutions. There is no solution. It is (6, 4). It is (4, 6).
Will someone PLEASE check my answers asap?? will mark a brainliest!!1) The graph of f(x) = (0.5)x is replaced by the graph of g(x) = (0.5)^x − k. If g(x) is obtained by shifting f(x) down by 3 units, the value of k is ____2) Find an equivalent function to f(x) = 4(7)2x. A) f(x) = 282xB) f(x) = 4(49)xC) f(x) = 196xD) f(x) = 16x(49)x3) The functions f(x) and g(x) are described using the following equation and table:f(x) = −6(1.02)^xx g(x)−1 −50 −31 −12 1Which equation best compares the y-intercepts of f(x) and g(x)?a) The y-intercept of f(x) is equal to the y-intercept of g(x).b) The y-intercept of f(x) is equal to 2 times the y-intercept of g(x).c) The y-intercept of g(x) is equal to 2 times the y-intercept of f(x).d) The y-intercept of g(x) is equal to 2 plus the y-intercept of f(x).4) What is the value of x in the solution to the following system of equations? (5 points)x − y = −3x + 3y = 5For #1 i put in 3 as the answer.For #2 i put B as the answer.For #3 i put B as the answer.For #4 i put 2 as the answer.
Travis took a taxicab from his office to a meeting on the other side of town. The cab ride cost $8.50 which includes a $2.00 tip. In deciman form, how far is it from his office to the meeting?
SOMEONE PLEASE HELP ;-;
What is the rate of change for this graph

14.42 Round to the nearest tenth.

Answers

The answer is 14.4 because if the last number is 5 or higher you round up if not you round down. Then, you should get 14.40 but, the 0 isn't necessary so the answer is 14.4.

The answer is 14.4, because when you round, if the number is 4 or lower, you make it a zero. If it is a 5 or higher, you make it a ten. But since it is a 2, you make it a zero, and 14.40 is the same as 14.4, because if you make it a fraction and simplify it, you still get the same as 14.4. So your answer is 14.4.

Answer : 14.4

Hope it works!!!

Roy's average balance checking account pays simple interest of 4.8% annually, and he made $2.25 in interest last month. What was Roy's average balance last month?

Answers

$562.50.

Thats what it is but it thinks im explaining it but im not because thats more than 20 characters

A circle has its center at the center of a square with 12-inch sides. Using 3.14 for pi, find the area of the square not covered by the circle, then write a ratio of the circle?s circumference to the perimeter of the square.

Answers

The area of the square notinside the circle is 30.96 in².

What is a circle?

A circle is a two-dimensional figure with a radius and circumference of 2πr.

The area of a circle is πr².

We have,

Square:

Side = 12 in

Area = 12²

Area = 12 x 12 = 144 in²

Circle:

Since the circle is inside the square.

Radius = 12/2 = 6 in

Area = πr² = 3.14 x 6 x 6 = 113.04 in²

Now,

The area of the square not inside the circle.

= Area of the square - Area of the circle

= 144 - 113.04

= 30.96 in²

Thus,

The area of the square notinside the circle is 30.96 in².

Learn more about circle here:

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So first, find the area of the square. 12x12= 144inches^2
Then find the area of the circle. To do this we use pi x r^2. The radius of the circle is 6 inches. Pi x 6^2 = 113.04inches^2.
144 - 113.04 = 30.6, so your answer is 30.6 inches^2

The circles circumference is worked out by using pi x d. The diameter is 12 inches, so 3.14x12 = 37.68 inches.
The squares perimeter is 12 x 4 = 48 inches.
If you round up the circumference of the circle to the nearest integer, you get 38 inches. The ratio would therefore be, 38:48, which can be rounded down to 19:24 :)

Give two different ratios with the description of a ratio relationship using the following information there are 15 male teachers in the school that 35 female teachers in the school

Answers

Two different ratio are;

Male teacher : Female teacher = 3 : 7

Male teacher : Teacher = 3 : 10

Here,

Number of male teachers = 15

Number of female teacher = 35

We have to find the two different ratio.

What is Ratio?

A ratio is a comparison of two similar quantities obtained by dividing one quantity by the other.

Now,

Number of male teachers = 15

Number of female teacher = 35

Hence, Number of total teacher = 15 + 35 = 50

So, Ratio of Male teacher to Female teacher = 15 : 35 = 3 : 7

And, Ratio of Male teacher to Teacher = 15 : 50 = 3 : 10

Therefore, Two different ratio are;

1. Male teacher : Female teacher = 3 : 7

2. Male teacher : Teacher = 3 : 10

Learn more about the ratio visit:

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Male teachers: female teachers
15:35
Simplifying
3: 7

The slope of line m is 7/8. If n⊥m, what is the slope of line n? A) 7/8
B) 8/7
C) -7/8
D) -8/7

Answers

$k:y=m_1x+b\nl:y=m_2x+c\n\nl\ \perp\ k\iff m_1m_2=-1$
We have:
$m_1=(7)/(8);\ m_2=?$
Substitute:
$(7)/(8)m_2=-1\ \ \ \ |\cdot(8)/(7)\n\nm_2=-(8)/(7)$
Answer: D)

Hey there !

When two lines are perpendicular , the product of their slope is -1 ,

m1 × m2 = -1
7/8 × m2 = -1

m2 = -8/7 Ans.

Given the following triangle, if c = 18.6 and m B = 43°, find the length of BC (side a) to the nearest whole number.