(Questions 8-10 use this.) X is the number of cars in a household in…

Step by step, with the reason for every step · AP Statistics Practice Exam 1 · AP Statistics

Step by step

The question

Question: x can be 0, 1, 2, 3, with probabilities 0.2, a missing one, 0.3, 0.1: find the missing probability.

x: 0, 1, 2, 3; P(x): 0.2, ?, 0.3, 0.1

There are four choices.

First we solve it, the normal way.

Then we pick.

1 All P(x) add to 1

x always takes one of its values.

So all the probabilities add up to 1.

a probability table always adds up to 1

0.2 plus P of 1 plus 0.3 plus 0.1 is 1.

0.2 + P(1) + 0.3 + 0.1 = 1

The known ones add up to 0.6.

0.6 + P(1) = 1

To remove the plus 0.6, we take away 0.6 on both sides.

1 minus 0.6 is 0.4.

P(1) = 1 − 0.6 = 0.4

Careful!

The missing probability is what is left over from 1.

Careful: the missing P is what is left of 1

2 Check

Let's check: 0.2 plus 0.4 plus 0.3 plus 0.1 is 1.

So it is right!

0.2 + 0.4 + 0.3 + 0.1 = 1

3 Pick the choice

Our answer is P(1) = 0.4.

That is choice A.

A) 0.4

4 Why not the others

B is 1.

Wrong: the total, not the missing part.

B) 1 ✗ the total, not the missing part

C is 0.25.

Wrong: split 1 equally: the probabilities add up to 1.

C) 0.25 ✗ split 1 equally: the probabilities add up to 1

D is 0.6.

Wrong: that is the sum of the others: take it away from 1.

D) 0.6 ✗ that is the sum of the others: take it away from 1

Let's look back.

First: all P(x) add to 1.

Then: check.

Then: pick the choice.

Last: why not the others.

Answer

P(1) = 1 − 0.6 = 0.4

Your turn

Try this one yourself, then check your answer:

X can be 0, 1, 2, 3, with probabilities 0.6, a missing one, 0.1, 0.2: find the x: 0, 1, 2, 3; P(x): 0.6, ?, 0.1, 0.2

Show the answer

P(1) = 0.1

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