x: 1, 2, 3; P(x): 0.5, ?, 0.2, find the missing probability

Step by step, with the reason for every step · Random variables · University Statistics

Step by step

Question: x can be 1, 2, 3, with probabilities 0.5, a missing one, 0.2: find the missing probability.

x: 1, 2, 3; P(x): 0.5, ?, 0.2

x always takes one of its values.

So all the probabilities add up to 1.

a probability table always adds up to 1

0.5 plus P of 2 plus 0.2 is 1.

0.5 + P(2) + 0.2 = 1

The known ones add up to 0.7.

0.7 + P(2) = 1

To remove the plus 0.7, we take away 0.7 on both sides.

1 minus 0.7 is 0.3.

P(2) = 1 − 0.7 = 0.3

Careful!

The missing probability is what is left over from 1.

Careful: the missing P is what is left of 1

Let's check: 0.5 plus 0.3 plus 0.2 is 1.

So it is right!

0.5 + 0.3 + 0.2 = 1

Let's look back.

First: all P(x) add to 1.

Last: check.

Answer

Careful: the missing P is what is left of 1

Try this one yourself, then check:

X can be 1, 2, 3, with probabilities 0.5, a missing one, 0.4: find the x: 1, 2, 3; P(x): 0.5, ?, 0.4

Show the answer

P(2) = 0.1