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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