ACT Math Review: Probability

P = \frac{outcomes you want}{total outcomes}

Worked examples

There are 8 marbles in total.

$P = \frac{3}{8}$

The outcomes are HH, HT, TH and TT.

Three of the four have a heads, so $P = \frac{3}{4}$ .

First pick: $\frac{3}{8}$

Second pick: 2 red remain out of 7, so $\frac{2}{7}$ .

$\frac{3}{8} \times \frac{2}{7} = \frac{3}{28}$

Without replacement, the chance of two reds is $\frac{3}{8} \times \frac{3}{8}$ .

That would be true only if you put the first marble back. Once it's gone, both the red count and the total go down.

A bag holds 4 green and 6 yellow. Find the chance of green.
Show answer
$\frac{2}{5}$
Flip two coins. Find the chance of two heads.
Show answer
$\frac{1}{4}$
A bag holds 5 red and 5 blue. Pick 2 without replacing. Find the chance both are red.
Show answer
$\frac{2}{9}$

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