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Of the 360 parts without surface aws, 18 are functionally defective and 342 are not. Therefore, P1D F 2 342 360 and P1D F 2 18 360

Random Samples from a Batch Recall that to select one item randomly from a batch implies that each item is equally likely. If more than one item is selected, randomly implies that each element of the sample space is equally likely. For example, when sample spaces were presented earlier in this chapter, sampling with and without replacement were de ned and illustrated for the simple case of a batch with three items {a, b, c}. If two items are selected randomly from this batch without replacement, each of the six outcomes in the ordered sample space Swithout 5ab, ac, ba, bc, ca, cb6

has probability 1 6. If the unordered sample space is used, each of the three outcomes in {{a, b}, {a, c}, {b, c}} has probability 1 3.

3 4 1 4

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What is the conditional probability that b is selected second given that a is selected rst Because this question considers the results of each pick, the ordered sample space is used. The de nition of conditional probability is applied as follows. Let E1 denote the event that the rst item selected is a and let E2 denote the event that the second item selected is b. Then, E1 5ab, ac6 and E2 5ab, cb6 and E1 E2 5ab6

The My Colors selections allow to you to change the effect of an image after it is taken Some settings change the entire look of the image, such as B/W or Sepia, while others alter the photo in more subtle ways by making only certain colors stand out My Colors adjustments are available in the Program AE, Shutter Priority, Aperture Priority, Manual, Movie, and Quick Shot modes and cannot be used in the Auto, Low Light, or Special Scenes modes Following is the list of options available in the My Colors settings In the My Colors menu while in Playback mode, use the 4-Way Controller to choose from the following options: Vivid Boosts contrast and color saturation to make the colors and crispness of your images pop A good setting to use in at light or low-contrast situations where colors may be muted Neutral.

When the sample space is larger, an alternative calculation is usually more convenient. For example, suppose that a batch contains 10 parts from tool 1 and 40 parts from tool 2. If two parts are selected randomly, without replacement, what is the conditional probability that a part from tool 2 is selected second given that a part from tool 1 is selected rst There are 50 possible parts to select rst and 49 to select second. Therefore, the (ordered) sample space has 50 49 2450 outcomes. Let E1 denote the event that the rst part is from tool 1 and E2 denote the event that the second part is from tool 2. As above, a count of the number of outcomes in E1 and the intersection is needed. Although the answer can be determined from this start, this type of question can be answered more easily with the following result.

... .

To select randomly implies that at each step of the sample, the items that remain in the batch are equally likely to be selected.

If a part from tool 1 were selected with the rst pick, 49 items would remain, 9 from tool 1 and 40 from tool 2, and they would be equally likely to be picked. Therefore, the probability that a part from tool 2 would be selected with the second pick given this rst pick is P1E2 E1 2 40 49.

In this manner, other probabilities can also be simpli ed. For example, let the event E consist of the outcomes with the rst selected part from tool 1 and the second part from tool 2. To determine the probability of E, consider each step. The probability that a part from tool 1 is selected with the rst pick is P1E1 2 10 50. The conditional probability that a part from tool 2 is selected with the second pick, given that a part from tool 1 is selected rst is P1E2 E1 2 40 49. Therefore, P1E2 P 1E2 0 E1 2P1E1 2 40 49 10 50 0.163

3 4 1 4

x 22

2 c1

... .

x 22

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