4. Probability Aa Aa sample space. The sum of The collection of all the possible

Question

4. Probability Aa Aa sample space. The sum of The collection of all the possible outcomes in an experiment is called the the probabilities of all outcomes must equal1.If an event is very unlikely to happen, its probability will be close to 0 If two events cannot occur at the same time, those events are said to be mutually exclusive._ If, however, an event's occurrence has no impact on another event, those two events are said to beindependent. Suppose you have two events that are equally likely to occur. This means both of their probabilities are 1 Experiment scenario: You are going to conduct a coin toss experiment using a fair, evenly balanced coin. Answer the following questions regarding your experiment: (Hint: You may find it valuable to write out the sample space of the experiment.) What is the probability of tossing "heads" on your first coin toss?0.50 What is the probability of tossing "heads" on each of your first two tosses? Experiment scenario: A new experiment involves rolling two fairly balanced, six-sided dice. A trial consists of tossing two dice, one after the other. There are 36 possible outcomes for each trial in this experiment. Answer the following questions regarding your experiment: (Hint: You may find it very valuable to write out the sample space of the experiment.) What is the probability of rolling a "3" and then a "3" in a trial? What is the probability of a trial resulting in a total score of 6? (Hint: In this case, "score" means the sum of the values on the two dice.) What is the probability of rolling a total score of 9 or greater?

Explanation / Answer

experiment scenario 1: probability of tossing heads on first coin toss =0.5

probabilty of tossing head on each of first two tossess =0.5*0.5=0.25

experiment scenario 2:

probabilty of rolling a 3 and then a 3 in a trail =(1/6)*(1/6)=1/36

probability of total resulting in total of 6 =5/36

probability of rolling a total score of 9 or greater =10/36 =5/18

probabilty of score greater then or equal 9 upon rolling a 5 with first die =2/6=1/3 (as second die should have 4 or 5 out of 6 outcomes)

for first die roll a 6; conditional probabilty =4/6 =2/3 (as second die can be 3,4,5,6 out of 6 outcomes)

conditional probability =0 (as maximum second die can have 6 which result in maximum sum of 8; hence we can not have sum 9 or greater)

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