Use the Following Methods to Illustrate the Sample Spaces of the Given Events

How do I determine the sample space of a given event? How do I determine the probability of an event to occur given the sample space? How do I determine the probability of two independent events? Chapter 14, Section D and E, Notes # ______

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
a) / c) / c)
b) / d) / d)
/ e) / e)

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
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

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() = ______or P(E not occurring) = ______– P(E occurring)

Independent Events: P(A and B) = ______ ______

How do I determine the sample space of a given event? How do I determine the probability of an event to occur given the sample space? How do I determine the probability of two independent events? Chapter 14, Section D and E, Notes # ______

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)
Ex 1: A coin and a die are tossed simultaneously. Determine the probability of getting a head and a 3 without using a grid.
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:
a)  they will be happy with the order of arrival
b)  they will be unhappy with the order of arrival
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:
a)  every time b) the first two times, but not on the third shot
b)  on no occasion