1. For tree diagrams the number of branches in the diagram is always the _______

Question

1. For tree diagrams the number of branches in the diagram is always the ________ the number of elements in the sample space.

A. Exactly equal to
B. Less than
C. A subset of
D. Greater than

2. According to the counting principle, if the first experiment can be performed 5 ways, and the second experiment can be performed 2 ways, how many ways can both experiments be performed (in that specific order)? ________________.

3. If a problem states that objects are chosen "without replacement", once a particular object has been picked, it can never be picked again.
True or False

4. Suppose that, for a certain experiment, the probability that a certain event never occurs is 0.26. What is the probability of that event happening at least once? __________.

Please fill in the blank

Explanation / Answer

1) For tree diagrams the number of branches in the diagram is always greater than the number of elements in the sample space. The number of terminal branches is equal to the number of elements in sample space.

2) First experiment is performed in 5 ways and second experiment is performed in 2 ways. Both the experiments must be performed in that specif order. So we use Counting Principle of Multiplication.

So, the number of ways in which both the experiments are performed in that specific order = 5 X 2 = 10 ways.

3) Without Replacement means if one particular object is picked, it will not be put back again in sample space for a second chance of selection, basically without repetition of objects.

So if a n object has been picked, it can never be picked again is True.

4) For a certain experiment, let A be the event mentioned in the question. Then P(A) is the probability of occurence of the event A. And AC is the complement of event A, so P(AC) is the probability of non-occurence of event A.

Given Probability that event never occurs is 0.26 i.e. P(AC) = 0.26

Using, P(A) + P(AC) = 1

P(A) + 0.26 = 1

P(A) = 1 - 0.26

P(A) = 0.74

So, Probability that event happens at least once is 0.74

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