The probability of 2 things happening:
The probability of 2 independent things happening either one after the
other or together is the probability of the first thing happening
multiplied by the probability of the second thing
Example 1: Flipping a coin 2 times:
What is the probability of flipping a coin 2 times and it coming up
"heads" both times?
1 1 1
Answer: --- X --- = --- or 1 chance in 4 tries
2 2 4
Note: This answer of 1/4 is correct before you make the first toss.
After you toss the coin once, and it comes up heads, the probability that
the second toss will also come up heads is 1/2 because the first toss is
in the past.
Example 2: Drawing 2 cards at the same time
What is the probability of drawing 2 aces in a row out of a deck
of 52 cards, if you don't put the first card back in the deck
before drawing the second card?
4 3 12 1
Answer: --- X --- = --- = --- or 1 chance in 221 tries
52 51 2652 221
Why is the probability of the second ace 3/51?
Well, after you draw the
first ace (you assume you got it) there are only 3 aces left and 51 cards.
Example 3: Drawing 2 cards with replacement:
How would the probabilities change if you had put the first ace back in
the deck before drawing the second time? Well, this makes the probability
of drawing an ace on the second draw the same as on the first draw, so the
probability of drawing 2 aces with replacement of the first ace
4 4 16 1
Answer: --- X --- = --- = --- or 1 chance in 169 tries
52 52 2704 169
Since 1/169 is larger than 1/221, this means you are more likely to get 2
aces in a row if you put your first ace back in the deck before you draw
your second card. But you knew that!
Probabilities as percents:|
Sometimes probabilities are given as percentages. This is just changing
the fraction we have been talking about into hundredths. So 1/2 becomes
50/100 or 50%. To change a fraction to a percent:
- Use your calculator to divide the numerator by the denominator
- Multiply the result by 100
So, to convert a probability of 2/7 to a percent:
- Divide the numerator by the denominator: 2 divided by 7 = .2857
- Multiply by 100: .2857 x 100 = 28.57 = 28.57%