Chance
plays a part in the outcomes of many events. The sex and eye color of a
baby, the numbers selected each week in Gold Lotto, the seat you are
allocated in an aircraft and the cards dealt in a game of blackjack are
all examples of situations where chance is involved in deciding what
happens.
Probability
The
probability of an event is the chance or likelihood of that event
occurring. We can describe probability using words such as those in the
following statements:
l“Australia is sure to win the next test match.”
l“I’ll probably pass that test.”
l“My boss says that I’m certain to get a pay
rise.”
l“Rain is likely on Tuesday.”
l“That’s impossible!”
l“I reckon you’ll get that part-time job.”
l“We’ve only got a 50-50 chance.”
Words
that are used to describe the chance of an event occurring are open to
interpretation. They can rely on the past experience and knowledge of the
person who says them. To be more precise and consistent when describing
the probability of an event, a numerical measure is applied.
The
numbers used to describe probability range from 0 for impossible up
to 1 for those events that are certain. The probability of all
other events must lie somewhere between these values.
Exercise:
1.Read the following statements:
(a)A coin will land with the head uppermost when tossed.
(b)I’ll not be a millionaire next year.
(c)Beethoven’s Fifth Symphony was written by Brahms.
(d)A man gives birth to a child.
(e)The sun will set at the end of the day.
(f)A baby that is born is a female.
(g)A student selected from your school is left handed.
Now
arrange the above statements in order of their likelihood. Place the
letters (a) to (g) on the following scale in the appropriate positions.
2.
Name two events that have a probability of on
3.Name
two events that have a probability of zero.
Equation:
In
any experiment, the probability that an event E occurs is given by
Example:
When
a child is born, we can assume that it is equally likely that the child
will be male or female. A woman has two children. Draw a tree diagram to
show the sex of the children and use it to find the probability that:
(a)both are female
(b)they are of different sexes.
Discussion:
1.
Combining Events
Jenny
had a problem. She wanted to go to a movie but couldn’t decide whether
to go by herself or with one of her friends——Linda,
Kate and Mary. After considering her dilemma, she decided to toss a coin
three times and then go to the movie according to the following outcomes:
Three heads ——Linda
Two heads—— Kate
One heads—— Mary
No heads—— Alone
She
thought that each of these outcomes would be equally likely, but after she
thought more about it she had the feeling that some outcomes were more
likely than others. To test her feeling, Jenny tossed a coin a number of
times and worked out that the outcomes could actually be achieved in the
following ways:
Linda(three heads) ——
Kate(two heads)——
Mary(one heads)——
Alone(no heads)——
Jenny
could have used a tree diagram to help see that the outcomes no heads, one
head, two heads and three heads are not equally likely in this situation.
The
tree diagram for three tosses of a normal coin is:
Jenny’s
examination revealed eight equally likely outcomes and the following
probabilities for the events listed:
P(going
with Linda)=
P(going
with Kate) =
P(going
with Mary)=
P(going
alone)=
2.
Should you stay or move?
There
are three boxes. Only one contains the orange. Guess which one contains
the orange. There’re 3 steps offered for you. After you finish these 3
steps, you must decide which box is your final choice.
