I need help

Question

1) A dating couple on The Amazing Race have a success rate of 65% of winning $1,000,000. There are eleven teams competing for a million

A). Find the probability that have exactly ten dating couples win a million dollars.

 

B). Find the probability that have at least six dating couples win a million dollars.

 

C). Find the probability that have no more than three dating couples win a million dollars.

 

D) Is the probability that have exactly have nine dating couple wins a million dollars likely?

 

Answer 1

Step 1:

In The Amazing Game, 11 couples had participated.

Success rate for one couple is 65% = 0.65.

Prize money for this competition is $1,000,000.

(A)

Find the probability that have exactly ten dating couples win a million dollars.

Since it follows binomial distribution,

The probability for k successes is .

Where n is number of samples(trails),

             p is probability of success,

             q is probability of failure.

The probability that have exactly ten dating couples win a million dollars is 0.052.

Solution:

The probability that have exactly ten dating couples win a million dollars is 0.052.

Answer 2

(B)

Step 1:

In The Amazing Game, 11 couples had participated.

Success rate for one couple is 65% = 0.65.

Prize money for this competition is $1,000,000.

Find the probability that have at least six dating couples win a million dollars.

Since it follows binomial distribution,

The probability for k successes is .

Where n is number of samples(trails),

             p is probability of success,

             q is probability of failure.

The probability that have at least six dating couples win a million dollars is 0.858.

Solution:

The probability that have at least six dating couples win a million dollars is 0.858.

Comments

Is there a faster way to solve this problem

---

Use the TI - 84 calculator to solve it in faster way.

---

Do I use pdf or cdf on the TI-84

---

1.binompdf()

It is used to find the probability for a specific random variable, x, that is a specific amount of successes.

binompdf(Number of total trails, probability of success, value of x)

 

2.binomcdf()

It is used to find the probability for x or fewer successes.

binomcdf(Number of total trails, probability of success, value of x to be less than or equal to)

 

So in this case you need to use binomcdf() function.

---

Do I use 1-p

---

I am so confused, I got 3.64

---

I think use have calculated for P(x<=6).

P(x<=6) = 0.331

But in the question asked for at least six.

So  1 - P(x<6)

= 1 - 0.148

= 0.85

---

How do you get 0.148

---

For P(x<6)

P(x<6) = P(x<=5)

You need to type in your calculator as shown below.

binomcdf(11,0.65,5)

Then you will get P(x<6) = 0.148.

Answer 3

(C)

Step 1:

In The Amazing Game, 11 couples had participated.

Success rate for one couple is 65% = 0.65.

Prize money for this competition is $1,000,000.

Find the probability that have no more than three dating couples win a million dollars.

Since it follows binomial distribution,

The probability for k successes is .

Where n is number of samples(trails),

             p is probability of success,

             q is probability of failure.

The probability that have no more than three dating couples win a million dollars is 0.01224.

Solution:

The probability that have no more than three dating couples win a million dollars is 0.01224.

Answer 4

(D)

Step 1:

In The Amazing Game, 11 couples had participated.

Success rate for one couple is 65% = 0.65.

Prize money for this competition is $1,000,000.
Find the probability that have exactly have nine dating couple wins a million dollars.

Since it follows binomial distribution,

The probability for k successes is .

Where n is number of samples(trails),

             p is probability of success,

             q is probability of failure.

The probability that have exactly have nine dating couple wins a million dollars is 0.1395.

Solution:

The probability that have exactly have nine dating couple wins a million dollars is 0.1395.

Comments

Is the event likely?

---

Equally likely events are events that have the same theoretical probability (or likelihood) of occurring.

The theoretical probabilities are as follows.

P(0) = 0.0000096

P(1) = 0.000197

P(2) = 0.00183

P(3) = 0.010203

P(4) = 0.037

P(5) = 0.098

P(6) = 0.183

P(7) = 0.242

P(8) = 0.225

P(9) = 0.139

P(10) = 0.0518

P(11) = 0.0087

As the theoretical Probabilities are not equal, the event is not equally likely.