'And' probabilities

Last updated: 9 Jul 2008

The probability two outcomes for independent events both occur can be found by multiplying their probabilities.

`P(text{A and B}) = P(A) xx P(B)`

What is the probability of throwing two heads in a row when tossing a coin?

This is the same as asking what the probability that the first coin tossed will be head AND the second coin tossed will be a head.

`P(text{two heads}) = P(text{first is head}) xx P(text{second is head})`

`P(text{two heads}) = 1/2 xx 1/2`

`P(text{two heads}) = 1/4`

So the probability that of tossing two heads in a row is 1/4.

A jar contains 2 red balls and 4 green balls. What is the probability that two balls selected at random from the jar are both green?

Each ball is equally likely to be selected from the jar so we can work out the probability of the first ball selected being green.

`P(text{first ball is green}) = text{number of green balls} / text{total number of balls}`

`P(text{first ball is green}) = 4/6 = 2/3`

Here is where we need to be careful, once we have taken 1 green ball out of the jar, the jar contains only 3 green balls and 2 red balls so

`P(text{second ball is green}) = text{number of green balls} / text{total number of balls}`

`P(text{second ball is green}) = 3/5`

Now we can say that

`P(text{both green}) = P(text{first is green} xx P(text{second is green})`

`P(text{both green}) = 2/3 xx 3/5 = 2/5`

So the probability that of picking out two green balls is 2/5.

You must log in or register to add a comment.