A Few Math Problems. Tricky, mind-goggling, but fun! You dont need to do all.?

I don't look for the quantity of the answer, i expect the quality.

2. A collection of five positive integers has mean 4.4, unique mode 3 and median 4. If an 8 is added to the collection, what is the new median? (Express as decimal to the nearest tenth.)

3. A magician designed an unfair coin so that the probability of getting a head on a flip is 60%. If he flips the coin three times, what is the probability that he flips more heads than tails. Express as common fraction.

4. Sue owns 11 pairs of shoes: 6 identical black pairs, three identical brown pairs and two identical gray pairs. If she picks two shoes at random, what is the probability that they are the same color and that one is a left shoe and the other is a right shoe? Common fraction, please.

7. What three-digit integer is equal to the sum of the factorials of its digits. (Factorials are n!)

8. How many distinct sums can be obtained by adding three different numbers from the set {-2,-1,1,2,3,4,5}

13. a bag contains 14 red marbles and 7 blue marbles. if exactly two marbles were to be selcted at random, without replacement, what is the probability that one would be red and one would be blue? Common fraction, please.

17. the mean of five positive integers is 1.5 times their median. four of the intetgers are 8, 18, 36, and 62, and the largest integer is not 62. What is the largest integer?

19. a data set for a class of 25 sixth graders has their ages listed as the integer values of either 10 or 11 years. the median age in the data set is 0.36 years greater than the mean. how many 10-year-olds?

Give a short explanation of show your work for each the best you can.

Disclaimer: I don't own these questions, my teacher passed them out. X3
 
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