JUST NEED PART D ....i have to put on WEBASSIGN ONLINE A box in a supply room co

Question

JUST NEED PART D ....i have to put on WEBASSIGN ONLINE

A box in a supply room contains 24 compact fluorescent lightbulbs, of which 8 are rated 13-watt, 9 are rated 18-watt, and 7 are rated 23-watt. Suppose that three of these bulbs are randomly selected. (a) What is the probability that exactly two of the selected bulbs are rated 23-watt? 0.1764 (b) What is the probability that all three of the bulbs have the same rating? 0.0865 (c) What is the probability that one bulb of each type is selected? 0.249 (d) If bulbs are selected one by one until a 23-watt bulb is obtained, what is the probability that it is necessary to examine at least 6 bulbs? 0.3648

Explanation / Answer

Answer to part d)

Given:

.

If the bulbs are selected one by one until 23 watt bulb is obtaained, Probability that at least 6 bulbs are taken out can be calculated in a different manner

P(at least 6 bulbs are selected ) = 1 - P(1) -P(2) - P(3) - P(4) - P(5)

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P(1) = only one bulb is selected , this is possible , when the first bulb is 23 watt

P(1 23 watt bulb) = 7/24 = 0.2917

.

P(2) = 2 bulbs are selected , this is possible when first bulb is not 23 watt , and the second bulb is 23 watt bulb

P(2) = (24-7)/24 * (7/23) = 119 / 552 = 0.2156

.

Likewise we calculate rest of the probabilites:

P(3) = (17 /24 * 16 /23 * 7 /22) = 0.1568

.

P(4) = (17 /24 * 16/23 * 15/22 * 7/21) = 0.112

.

P(5) = (17/24 *16/23 * 15/22 *14/21 * 7/20) = 0.0784

.

P(atleast 6) = 1 - 0.2917 - 0.2156 - 0.1568 - 0.1120 - 0.0784

P(atleast 6) = 0.1455 = 0.146 (rounded to 3 decimal places)

Thus the answer to part d is 0.146

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