Math Is Fun Forum

MellyBigD

Member

Registered: 2018-03-13

Posts: 10

Statistics Probability

Hi there Everyone

I'm from South Africa and doing a modules: Business Statistics.

For some reason I just don't get probability, maybe it's cause I have this mind block?!? But I want to master it!

Please help me with these exercises:

A well-known business school in Cape Town conducted a survey in 2013 amongst its MBA applicants to determine whether students apply to only one business school.  A sample of 2018 students was chosen and the following results were obtained: (rounded to 3 decimals)

Age    Did you apply to more than one school?    
    Yes    No    Total
23 and under    207    201    408
24-26    299    379    678
27-30    185    268    453
31-35    66    193    259
36 and over    51    169    220
Total    808    1210    2018

1.1) What is the probability that a randomly selected applicant is younger than 27                     [1]

1.2) What is the probability that a randomly selected applicant is 24-26 years old given that he/she did not apply to more than one school?                                                                 [3]

1.3) What is the probability that a randomly selected applicant is 24-26 years old or did not apply to more than one school?                                                                                       [3]

1.4) Is the number of schools applied to independent of age? Let A = “Yes” and B = “23 and under”.    [3]

                                       

Question 2 [10 Marks]

The probability that a flight departs on time in 0.83 and the probability that it arrives on time is 0.92.  The probability that the flight arrived on time given that it departed on time is 0.94 (rounded off to two decimals).

2.1) What is the probability that the flight did not arrive on time?                                           [1]

2.2) What is the probability that the flight arrived and departed on time?                             [3]

2.3) What is the probability that the flight departed on time given that it has arrived on time?        [3]

2.4) What is the probability that the flight either arrived or departed on time?                    [3]

Question 3 [10 Marks]

Guess clothing stores recorded the buying behaviour of their customers over the last decade (2004 to 2014). They established that the probability that a customer will buy a pair of Guess jeans is about 0.7. A customer buys a Guess top 30% of the time given that a pair of Guess jeans was purchased, but only 15% of the time given that a pair of Guess jeans was not purchased.

3.1) Explain the concepts of:
3.1.1) Probability Addition Law                                    (2)

3.1.2) Probability Multiplication Law                                                 (2)

3.2) Calculate the probability that a randomly selected person buys a pair of Guess jeans and a Guess top    (rounded off to two decimals).                                           (3)

3.3) Calculate the probability that a randomly selected person buys a Guess top but no pair of Guess jeans (rounded off to two decimals).                                          (3)

TOTAL MARKS = 30

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,406

Re: Statistics Probability

Hi MellyBigD,

Welcome to the forum!

People would help up with some hints and explanations. The homework and exercises are to be done by themselves.

---

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

MellyBigD

Member

Registered: 2018-03-13

Posts: 10

Re: Statistics Probability

Thanks, Ganesh

Noted,
Kind regards

Mathegocart

Member

Registered: 2012-04-29

Posts: 2,226

Re: Statistics Probability

Hi, spamming multiple threads with the same problems does not accelerate the rate at which we solve your problems.

---

The integral of hope is reality.
May bobbym have a wonderful time in the pearly gates of heaven.
He will be sorely missed.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Statistics Probability

hi MellyBigD

Welcome to the forum.

A well-known business school in Cape Town conducted a survey in 2013 amongst its MBA applicants to determine whether students apply to only one business school.  A sample of 2018 students was chosen and the following results were obtained: (rounded to 3 decimals)

Age    Did you apply to more than one school?     
                                             Yes                     No                 Total
23 and under                          207                   201                 408
24-26                                     299                  379                  678
27-30                                     185                  268                  453
31-35                                      66                   193                  259
36 and over                              51                  169                   220
Total                                      808                 1210                 2018

1.1) What is the probability that a randomly selected applicant is younger than 27                     [1]

Any probability is <number where the chosen event occurs divided by <total of all possible events>

So add up how many are younger than 27 and divide by the total number of applicants.

1.2) What is the probability that a randomly selected applicant is 24-26 years old given that he/she did not apply to more than one school?                                                                 [3]

As we are told the applicant did not apply to more than one, you should confine the calculations to the numbers in the 'No' column.  In all other respects this is the same as part 1.1

1.3) What is the probability that a randomly selected applicant is 24-26 years old or did not apply to more than one school?                                                                                       [3]

Now the event that satisfies the question includes two groups, so add together '24-26' group to the 'no' group.

1.4) Is the number of schools applied to independent of age? Let A = “Yes” and B = “23 and under”.    [3]

To be 'independent' the probability taking age into account must be the same as the probability if we ignore age.  If you're told to take A as 'yes' and B as '23 and under', I think the questioner intends that you just consider the B group and ask is the probability the same for this limited group.  It looks like you've been given a formula for this involving A and B so you should be able to plug in the numbers.

So B' is the number not '23 and under'

So is P(A given B) the same as P(A given not B)

Please have a try at these and post back your answers.  Once you're ok with them we can move on to another question.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

MellyBigD

Member

Registered: 2018-03-13

Posts: 10

Re: Statistics Probability

Thanks Bob, I will go through the theory again so I can have a good grasp of the concepts. Only then will I refer back and attempt these questions.

Thanks again,

Libera

Member

Registered: 2018-03-07

Posts: 16

Re: Statistics Probability

Thanks Bob, I will go through the theory again so I can have a good grasp of the concepts. Only then will I refer back and attempt these questions.

Thanks again,

But you have not to throw everything away: you've already answered Yesterday 01:15:29 in your previous topic - urging is confusing, do you agree? -
1.1 P(A) = 408+678/2018 = 0.538
1.2 P(AlB) = 379/2018 / 1210/2018 = 0313
1.3 P(AUB) = P(A) + P(B) - P(AandB) =  (678/2018)+(379/2018)-(379/2018) = 0336
1.4 P(A) *P(B) = (207/808) * (408/2018) = 0.0517 interpretation

I add a question: does 0.0517 here above express something about in/dipendence between number of schools and age? Otherwise, what does it express?

In my opinion you are ready to face also question 2: would you try?