Sample Space
Sample Space: __________________________________________________________________
Use the following methods to illustrate the sample spaces of the given events:
a) Tossing a coin c) Tossing 2 coins
b) Rolling a die d) Drawing 2 marbles from bag containing a number of red, green, and yellow marbles
e) The winners of 2 players playing a tennis match where the person who wins 2 out of 3 sets wins.
|Listing Outcomes |2 Dimensional Grids |Tree Diagrams |
| |c) |c) |
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| |d) |d) |
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| |e) |e) |
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You Do:
|Listing Outcomes |2 Dimensional Grids |Tree Diagrams |
|The order in which 3 blocks A, B, C can be lined up |Rolling a die and tossing a coin simultaneously |Tossing a 5 cent coin and a 10 cent coin simultaneously |
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| The sexes of a 2 child family |Rolling a die and spinning a spinner with sides A, B |Drawing two tickets from a hat containing a number of pink, |
| | |blue, and white tickets |
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Theoretical probability: P(E) = _____________________________________
P(No chance of an event occurring) : __________ P(an event is certain to occur) ____________
For any event E : _______ ≤ P(E) ≤ ________
Complementary Events: P(E) + P([pic]) = _________ or P(E not occurring) = ________ – P(E occurring)
Independent Events: P(A and B) = ____________ [pic] ____________
Using the rule of theoretical probability and sample space answer the following questions:
Step 1: Represent the sample space using the easiest method.
Step 2: Use the formula for theoretical probability to find the probability.
1) A ticket is randomly selected from a basket containing 3 green, 4 yellow, and 5 blue tickets.
Sample Space ___________________________________________
Determine the probability of getting:
a) a green ticket b) a green or yellow ticket c) an orange ticket d) a green, yellow, or blue ticket
_______________ _______________ _______________ ________________
2) You roll two dice and record the sum of the dice .
Determine the chance of:
a) getting a sum of 6 __________________
b) not getting a sum of 6 _________________
c) Rolling a sum larger than 5 ________________
3) Show a tree diagram determining the chances of rain on two consecutive days.
Find the probability that it rains:
a) Two days in a row _______________
b) At least one of the days ________________
c) On the second day ________________
|Independent Events: P(A and B) = P(A) · P(B) |
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|Ex 1: A coin and a die are tossed simultaneously. Determine the probability of getting a head and a 3 without using a grid. |
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|Ex 2: A couple decided that they want 4 children, none of whom will be adopted. They will be disappointed if the children are not born in the|
|order boy, girl, boy, girl. Determine the probability that: |
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|they will be happy with the order of arrival |
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|they will be unhappy with the order of arrival |
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|You Do: An archer always hits a circular target with each arrow shot, and hits the bullseye 2 out of every 5 shots on average. If 3 arrows |
|are shot at the target, determine the probability that the bullseye is hit: |
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|every time b) the first two times, but not on the third shot |
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|on no occasion |
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Sample space for 2)
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