Independent Probability: A Fair Coin Toss
What are the chances?
the number of ways the outcome can occur
probability of an outcome =
Probability is a ratio.
the number of all possible outcomes
Study this chart:
heads
tails
H
T
Single-Coin Toss
A coin has two sides. One side is
heads and the other is tails.
Now complete this table about the Single-Coin Toss:
Tossing One Coin
How many possible outcomes are there?
What are those possible outcomes?
What’s the probability of the coin landing heads up?
What’s the probability of the coin landing tails up?
What’s the probability of the coin landing neither
heads up nor tails up?
What’s the probability of the coin landing either heads
up or tails up?
Study this chart about a double-coin toss:
heads
tails
heads
HH
HT
tails
TH
TT
Double-Coin Toss
Each coin has two sides:
heads and tails.
Now complete this table about the double-coin toss:
Tossing One Coin
How many possible outcomes are there?
What are those possible outcomes?
What’s the probability of both coins landing heads up?
What’s the probability of both coins landing tails up?
What’s the probability of one coin landing heads up
and the other coin landing tails up?
What’s the probability of neither coin landing heads
up?
What’s the probability of neither coin landing tails up?
Now, imagine a number cube. It has six sides, and the sides are numbered consecutively 1 through 6.
Complete this table about rolling a number cube:
Rolling a Number Cube
How many possible outcomes are there?
What are those possible outcomes?
What’s the probability of the cube landing with the
number 1 face up?
What’s the probability of the cube landing with the
number 2 face up?
What’s the probability of the cube landing with the
number 3 face up?
What’s the probability of the cube landing with the
number 4 face up?
What’s the probability of the cube landing with the
number 5 face up?
What’s the probability of the cube landing with the
number 6 face up?
What’s the probability of the cube landing with an
even number face up?
What’s the probability of the cube landing with an odd
number face up?
What’s the probability of the cube landing with the
number 4 face up?
What’s the probability of the cube landing with
neither an even nor an odd number face up?
Consider a bag of marbles…
There are 100 marbles in a bag. Twenty-five of them are red. Twenty-five of them are blue. Twenty-five
of them are yellow, and twenty-five of them are green. If I reach into the bag without looking, what is
the probability that I will pull out a red marble?
the number of red marbles
probability of pulling a red
=
marble out of the bag
=
the total number of marbles
25
100
=
1
4
Indeed, 25/100 is an accurate ratio that shows the likelihood that I will pull a red marble out of the bag,
but I should show this in lowest terms. In other words, ¼ is the preferred way of telling the likelihood
that I will pull a red marble out of the bag.
As a percent, I can then say the likelihood that I will pull a red marble out of the bag is 25%. I can convert
¼ into a percent: 1 divided by 4 is .25, and .25 x 100 = 25.
Answer these questions:
Pulling a Marble out of a Bag
What’s the probability that I will pull a blue marble out
of the bag (as a ratio and as a percentage)?
What’s the probability that I will pull either a yellow
marble or a green marble out of the bag (as a ratio
and as a percentage)?
What’s the probability that I will pull a blue marble, a
yellow marble, or a green marble out of the bag (as a
ratio and as a percentage)?
For additional practice with Independent Probability, try these:
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“Days in a Week”
“Deck of Cards”
“Spinner with Colors”
“Pair of Coins”