Math 205

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Your Name: Jennifer Green MAT 205 Final Examination
Your Score: of 250 points

NOTE: You must show your work on each problem to receive full credit points allocated for each problem (excluding T/F questions)

Write a matrix to display the information.
1) At a store, Sam bought 3 batteries, 15 60-watt light bulbs, 46 100-watt light bulbs, 8 picture-hanging kits, and a hammer. Jennifer bought 12 batteries, 3 100-watt light bulbs, and a package of tacks. Write the information as a 2 x 6 matrix.

| |BATTERIES |60watt light bulbs |100 watt light bulbs |Picture hanging kits |Hammer |Package of tacks | |Sam |3 |15 |46 |8 |1 |0 | |Jennifer |12 |0 |3 |0 |0 |1 |

In a certain distribution, the mean is 50 with a standard deviation of 6. Use Chebyshev's theorem to tell the probability that a number lies in the following interval. Round your results to the nearest whole percent. 2) Between 35 and 65

Ans: we have z = (35-50)/6 = -2.5 and z = (65-50)/6 = 2.5
So 35 and 65 lies within 2.5 standard deviation of mean
By Chebyshev’s theorem we have the probability as 1 -1/k2 , where k is the standard deviation within which the numbers In this case k = 2.5
So the required probability = 1 -1/2.52
=> 0.84
=>at least 84%

A die is rolled five times and the number of twos that come up is tallied. Find the probability of getting the indicated result. 3) Two comes up one time.
Ans: This is an example of binomial distribution
Probability of occurance of 2, p = ½
Probability of non-occurrence of 2, q = 1-1/2 =1/2
So the probability that two comes 1 times (which means it doesn’t appear on other 4 occaisions) ⇨ C(5,1) p1q4
⇨ 5(1/6)(5/6)4
⇨ 0.402 is the required probability

Find the indicated probability.
4) If three cards are drawn without replacement from an ordinary deck, find the probability that the third card is a face card, given that the first card was a queen and the second card was a 5. Ans:

Now third should be a face card, we have already drawn one face card (queen), so remaining face cards are 11 (ace is not being considered as face card), total remaining cards are 50 So the probability that it’s a face card is 11/50

A die is rolled twice. Write the indicated event in set notation. 5) Both rolls are even.
The possible even numbers are 2, 4,6 and so the events will be {(2,2),(2,4), (2,6),(4,2),(4,4),(4,6),(6,2),(6,4),(6,6)}

Find the indicated probability.
6) If two cards are drawn without replacement from an ordinary deck, find the probability that the second card is red, given that the first card was a heart.
Ans: total number of red cards = 26
First was a heart, so remaining red cards = 25
So the probability that the second card is red given that first card was a heart = 25/51 How many distinguishable permutations of letters are possible in the word? 7) COMMITTEE
There are a total of 9 words, so 9! Is the total possibility , in this M , T and E are repeated twice, so the number of Distinguishable permutations are

9!/(2!x2!x2!) => 45360

Solve the problem.
8) A restaurant offers 8 possible appetizers, 13 possible main courses, and 7 possible desserts. How many different meals are possible at this restaurant?
(Two meals are considered different unless all three courses are the same). 8x13x7 => 728 possibilities

Four accounting majors, two economics majors, and three marketing majors have interviewed for five different positions with a large company. Find the number of different ways that five of these could be hired. 9) There is no restriction on the college majors hired for the five positions. There is no restriction on the college majors hired...
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