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danylop26 danylop26

10-06-2022
Mathematics

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MrRoyal MrRoyal · Answer 1 · 2022-06-11T08:45:36+02:00

The questions are illustrations of probability and the usage of two-way tables

The survey of 1000 Argyle student

To do this, we make use of the following representations:

x represent owning a cell phone (x' is its complement).
y represent owning a PS5 (y' is its complement).

So, the given parameters are:

Total = 1000

x = 781

x and y = 133

x' and y' = 192

Using the above data values, we have:

y = Total - x

x and y' = x - x and y

x' and y = y - x' and y'

This gives

y = 1000 - 781 = 219

x and y' = 781 - 133 = 648

x' and y = 219 - 192 = 27

See attachment for the complete table.

The probability of cats

Probability that cats prefer flying

This is calculated as:

P = Flying/Total

So, we have:

P = 20/100 = 1/5

Probability that a selected cat is an alley cat

This is calculated as:

P = Alley Cat/Total

So, we have:

P = 41/100

Probability that a selected alley cat prefers invisibility

This is calculated as:

P = Alley Cat and Invisible/Alley Cat

So, we have:

P = 21/41

Probability that a selected home cat prefers invisibility

This is calculated as:

P = Home Cat and Invisible/Home Cat

So, we have:

P = 22/59

Ice cream flavors

Probability of Peanut Butter Crunch

The given parameters are:

Peanut Butter Crunch = 1

Flavors = 52

This probability is then calculated as:

P = Peanut Butter Crunch/Total

So, we have:

P = 1/52

Theoretical probability of Cotton Candy

In this case, we have:

Cotton Candy = 1

Flavors = 5

This probability is then calculated as:

P = Cotton Candy/Flavors

So, we have:

P = 1/5

Experimental probability of Mango

In this case, we use the table results i.e.

Mango = 1

Friends = 15

This probability is then calculated as:

P = Mango/Friends

So, we have:

P = 1/15

Hence, the experimental probability of Mango is 1/15