Probability

[DylsexicChciken]

In a small city, approximately 32% of those eligible are called for jury duty in any one calendar year. People are selected for jury duty at random from those eligible, and the same individual cannot be called more than once in the same year.

 

(a) What is the probability that a particular eligible person in this city is selected two years in a row?

 

The answer turns out to be 0.32 * 0.32 =0.1024=(32/100)*(32/100). Why is this the answer?

 

At first I thought it should be (32/100) = 0.32. This is because after we select the first 32 people out of 100 for jury duty, there is a (32/100) chance we select the same person from last year's 32 people. Why do we multiply 0.32 * 0.32?

Edited October 13, 2014 by DylsexicChciken

[Robittybob1]

In a small city, approximately 32% of those eligible are called for jury duty in any one calendar year. People are selected for jury duty at random from those eligible, and the same individual cannot be called more than once in the same year.

 

(a) What is the probability that a particular eligible person in this city is selected two years in a row?

 

The answer turns out to be 0.32 * 0.32 =0.1024=(32/100)*(32/100). Why is this the answer?

 

At first I thought it should be (32/100) = 0.32. This is because after we select the first 32 people out of 100 for jury duty, there is a (32/100) chance we select the same person from last year's 32 people. Why do we multiply 0.32 * 0.32?

Because there is a 32% chance of being selected in each year.

[studiot]

 

At first I thought it should be (32/100) = 0.32. This is because after we select the first 32 people out of 100 for jury duty, there is a (32/100) chance we select the same person from last year's 32 people. Why do we multiply 0.32 * 0.32?

 

 

Consider the selection of one single juror.

 

Because there are two probability dependent 'trials or experiments' (the correct statistical words for selection) to consider.

One for each year.

The combined effect of probability in both trials has to be taken into account.

 

Here is a sequence using Venn diagrams to show why the probability is the product of the individual probabilities.

 

Start with the first year and select 32%. (Fig1) Say the population is 100 so 32 citizens are selected.

 

The only jurors who can be selected both years will come from this 32%. (Fig2)

 

So in the second year select 32% of these 32 (Fig3) ie 10 citizens.

 

Now 32% of something is an old fashioned way of saying multiply by 0.32.

 

So 32% of (32%) = (0.32 x 0.32) = 0.1024.

 

Note that the 68 citizens who were not selected in the first year also have a 32% probability of being selected in the second year

So by the same reasoning 0.32 x 68 = 22 citizens were not selected in the first year but selected in the second.

 

Note that 10 + 22 = 32. That is the probability of being slected in the second year is 32% as expected.

 

Edited October 13, 2014 by studiot

[Relative]

I love probability , some one mentions 32% probability of been selected, untrue in my opinion when random is random,, and random does not have set rules , even probabilities are not accurate in a random system.

[imatfaal]

!

Moderator Note

 

Relative - your guesses and vague notions are not acceptable when answering a question in homework help. Do not answer questions unless you have an idea about the topic. Do not respond to this moderation with the thread.

 

[DylsexicChciken]

 

Consider the selection of one single juror.

 

Because there are two probability dependent 'trials or experiments' (the correct statistical words for selection) to consider.

One for each year.

The combined effect of probability in both trials has to be taken into account.

 

Here is a sequence using Venn diagrams to show why the probability is the product of the individual probabilities.

 

Start with the first year and select 32%. (Fig1) Say the population is 100 so 32 citizens are selected.

 

The only jurors who can be selected both years will come from this 32%. (Fig2)

 

So in the second year select 32% of these 32 (Fig3) ie 10 citizens.

 

Now 32% of something is an old fashioned way of saying multiply by 0.32.

 

So 32% of (32%) = (0.32 x 0.32) = 0.1024.

 

Note that the 68 citizens who were not selected in the first year also have a 32% probability of being selected in the second year

So by the same reasoning 0.32 x 68 = 22 citizens were not selected in the first year but selected in the second.

 

Note that 10 + 22 = 32. That is the probability of being slected in the second year is 32% as expected.

 

probab1.jpg

 

A question about the diagram. Aren't we selecting 32% from the total population each year, for example 32 out of 100 people for first year and 32 out of same 100 for the second year. So why are we taking 32% of the 32 selected from last year for the second year, instead of 32% of 100 for the second year?

[studiot]

That was why I added the bit about the selection in the second year being partly from those who has been selected before and those who had not been selected.

The total of these must add up to 32% of the total population.

 

However they have the same probability of selection the second year, whether they have been selected before or not.