How Do Marbles Play In Removing Illiteracy
TREE DIAGRAMS AND BINOMIAL PROBABILITIES (Chapter 20)
Example 2
405
Self Tutor
John plays Peter at tennis. The first to win two sets wins the match.
Illustrate the sample space using a tree diagram.
If J means “John wins the set” and P means “Peter wins the set” then the tree diagram is:
1st set
2nd set
3rd set
J
J
J
P
P
J
We could write the sample space in set notation as
S = fJJ, JPJ, JPP, PJJ, PJP, PPg.
J
P
P
P
2 Use a tree diagram to illustrate the sample space for the following: a The genders of a 4-child family. b Bag A contains red and white marbles and bag B contains blue and yellow marbles.
A bag is selected and one marble is taken from it. c Hats A, B and C each contain pink and purple tickets. A hat is selected and …show more content…
In such a case we say we have dependent events.
Two or more events are dependent if they are not independent.
Dependent events are events where the occurrence of one of the events does affect the occurrence of the other event.
If A and B are dependent events then
P(A then B) = P(A) £ P(B given that A has occurred).
A typical example of dependent events is when we sample two objects without replacement.
This means that the first object is not replaced before the second is selected. It therefore cannot be selected twice.
Example 4
Self Tutor
A box contains 4 red and 2 yellow tickets. Two tickets are randomly selected one after the other from the box, without replacement. a Display this information on a tree diagram. b What is the probability that both are red? c What is the probability that one is red and the other is yellow? a Let R be the event that a red ticket is drawn and Y be the event that a yellow ticket is drawn.
Note that the outcome of the second event depends on the first.
1st selection
Example 2
405
Self Tutor
John plays Peter at tennis. The first to win two sets wins the match.
Illustrate the sample space using a tree diagram.
If J means “John wins the set” and P means “Peter wins the set” then the tree diagram is:
1st set
2nd set
3rd set
J
J
J
P
P
J
We could write the sample space in set notation as
S = fJJ, JPJ, JPP, PJJ, PJP, PPg.
J
P
P
P
2 Use a tree diagram to illustrate the sample space for the following: a The genders of a 4-child family. b Bag A contains red and white marbles and bag B contains blue and yellow marbles.
A bag is selected and one marble is taken from it. c Hats A, B and C each contain pink and purple tickets. A hat is selected and …show more content…
In such a case we say we have dependent events.
Two or more events are dependent if they are not independent.
Dependent events are events where the occurrence of one of the events does affect the occurrence of the other event.
If A and B are dependent events then
P(A then B) = P(A) £ P(B given that A has occurred).
A typical example of dependent events is when we sample two objects without replacement.
This means that the first object is not replaced before the second is selected. It therefore cannot be selected twice.
Example 4
Self Tutor
A box contains 4 red and 2 yellow tickets. Two tickets are randomly selected one after the other from the box, without replacement. a Display this information on a tree diagram. b What is the probability that both are red? c What is the probability that one is red and the other is yellow? a Let R be the event that a red ticket is drawn and Y be the event that a yellow ticket is drawn.
Note that the outcome of the second event depends on the first.
1st selection