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Background: The theoretical probability of getting a head on a single toss of a fair coin is ½ where there 1 represents the occurrence of a head and the 2 represents all the possible outcomes of a single coin toss. 1 = a head occurs 2 = all possible outcomes of a single coin toss All possible outcomes can also be expressed as the sample space for a given problem. This sample space can be indicated by including all possible outcomes in parenthesis, e.g. (H,T). To carry this example further, what are all possible combinations of heads and tails (or outcomes) for two tosses of the same coin? One way to determine this is to set up a Punnett Square on which you put all possible outcomes for the first toss onto the horizontal axis and all possible outcomes for the second toss onto the vertical axis. All outcomes of 2 tosses of one coin Second Toss (Probability) First Toss (Probability) H (½) T (½) H (½) HH (¼) TH (¼) T (½) HT (¼) TT (¼) In this example, the number (½) indicates the probability of tossing a head or a tail on a single toss of a coin. Also, the outcome of the first toss is independent of the outcome of the second toss. When two outcomes are independent of each other, the probability of both occurring is equal to the probability of the first outcome occurring (a head or a tail) times the probability of the second outcome occurring (a head or a tail), e.g., the probability of getting a head on the first toss and a tail on the second toss is equal to ½ times ½, or ¼. Note: you can also determine these probabilities by counting the number of boxes in the Punnett square that represents a specific outcome of two tosses of a coin (e.g. HH= one of the boxes) and dividing this by the total number of boxes (4) in the Punnett square. a. What is the probability that the first toss of a coin will be H and the second toss will be T? What is the probability that you toss one head and one tail (in any order)? What is the probability that you toss two heads in a row? What is the probability that you toss two tails in a row? What is the probability that you toss either two heads in a row or two tails in a row?

          Background: The theoretical probability of
getting a head on a single toss of a fair coin is ½ where there 1
represents the occurrence of a head and the 2 represents all the
possible outcomes of a single coin toss.
             
1 = a head occurs
             
2 = all possible outcomes of a single coin toss
All possible outcomes can also be expressed as the
sample space for a given problem. This sample
space can be indicated by including all possible outcomes in
parenthesis, e.g. (H,T). To carry this example
further, what are all possible combinations of heads and tails (or
outcomes) for two tosses of the same coin? One way to determine
this is to set up a Punnett Square on which you
put all possible outcomes for the first toss onto the horizontal
axis and all possible outcomes for the second toss onto the
vertical axis.
All outcomes of 2 tosses of one coin
Second Toss (Probability)
First Toss (Probability)
H (½)
             
T (½)
H (½)
HH (¼)
             
TH (¼)
T (½)
         HT
(¼)
             
TT (¼)
In this example, the number (½) indicates the probability of
tossing a head or a tail on a single toss of a coin. Also, the
outcome of the first toss is independent of the outcome of the
second toss. When two outcomes are independent of each other, the
probability of both occurring is equal to the
probability of the first outcome occurring (a head or a tail) times
the probability of the second outcome occurring (a head or a tail),
e.g., the probability of getting a head on the first toss and a
tail on the second toss is equal to ½ times ½, or ¼. Note: you can
also determine these probabilities by counting the number of boxes
in the Punnett square that represents a specific outcome of two
tosses of a coin (e.g. HH= one of the boxes) and dividing this by
the total number of boxes (4) in the Punnett square.
a. What is the probability that the first toss of a coin will be
H and the second toss will be T?
What is the probability that you toss one head and one tail (in
any order)?
What is the probability that you toss two heads in a row?
What is the probability that you toss two tails in a row?
What is the probability that you toss either two heads in a row
or two tails in a row?

Added by Shawn A.

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