KS4 Grade 10 - PROBABILITY
Lesson 2...TREE DIAGRAMS
![Picture](/uploads/1/3/3/4/13343229/9414655.gif?168)
TREE DIAGRAMS are highly useful for diagrammatically representing the possible variety of outcomes of various events and their associated probabilities, particularly when two or more events occur together
The tree diagram on the left shows the possible outcomes for the following scenario:
A bag contains a red ball, a white ball and a green ball. A ball is chosen randomly from the bag and then replaced. Another ball is then randomly selected. Demonstrate the possible outcomes using a tree diagram.
As can be seen, there are 9 potential outcomes, all with an equal chance of 1/9 of occurring.
Eg. Find the probability of choosing 2 balls of the same colour.
P(RR or WW or GG) = 1/9 + 1/9 + 1/9 = 3/9 = 1/3
TASK 1 - Textbook Pg355 Ex10
HOMEWORK - Holiday HMWK WS
The tree diagram on the left shows the possible outcomes for the following scenario:
A bag contains a red ball, a white ball and a green ball. A ball is chosen randomly from the bag and then replaced. Another ball is then randomly selected. Demonstrate the possible outcomes using a tree diagram.
As can be seen, there are 9 potential outcomes, all with an equal chance of 1/9 of occurring.
Eg. Find the probability of choosing 2 balls of the same colour.
P(RR or WW or GG) = 1/9 + 1/9 + 1/9 = 3/9 = 1/3
TASK 1 - Textbook Pg355 Ex10
HOMEWORK - Holiday HMWK WS
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g10_hw_holidays.pdf | |
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Lesson 1...SIMPLE PROBABILITY, EXCLUSIVE AND INDEPENDENT EVENTS
![Picture](/uploads/1/3/3/4/13343229/6243967.jpg?345)
PROBABILITY is the study of chance.
Suppose a event can have 'n' equally likely results and 's' number of favourable results, then the probability of 's' occurring is
P(s) = s/n
If an event cannot happen it has a probability of 0
If an event is certain to happen it has a probability of 1
All other probabilities lie between 0 and 1 (see image on left)
Eg. Probability of rolling an even number on a standard 6-sided dice is
P(even) = 3/6 = 1/2 or 0.5 or 50%
Two events are EXCLUSIVE if they cannot occur at the same time. The 'OR' rule gives
P(A or B) = P(A) + P(B)
Two events are INDEPENDENT if the occurrence of one event is unaffected by the occurrence of the other. The 'AND' rule gives
P(A and B) = P(A) x P(B)
TASK 1 - Textbook Pg351 Ex8
TASK 2 - Textbook Pg354 Ex9
HOMEWORK - Ch10 Final HMWK WS
Suppose a event can have 'n' equally likely results and 's' number of favourable results, then the probability of 's' occurring is
P(s) = s/n
If an event cannot happen it has a probability of 0
If an event is certain to happen it has a probability of 1
All other probabilities lie between 0 and 1 (see image on left)
Eg. Probability of rolling an even number on a standard 6-sided dice is
P(even) = 3/6 = 1/2 or 0.5 or 50%
Two events are EXCLUSIVE if they cannot occur at the same time. The 'OR' rule gives
P(A or B) = P(A) + P(B)
Two events are INDEPENDENT if the occurrence of one event is unaffected by the occurrence of the other. The 'AND' rule gives
P(A and B) = P(A) x P(B)
TASK 1 - Textbook Pg351 Ex8
TASK 2 - Textbook Pg354 Ex9
HOMEWORK - Ch10 Final HMWK WS
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chapter_10final_hw.pdf | |
File Size: | 517 kb |
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