Little bit of probability...

Questions :

1) A jar contains four blue marbles and two green marbles. Without looking, two marbles are drawn from the jar. What is the probability that two marbles with the same color will be selected?

2) How many different ways can 6 people arrange themselves inside a small plane if two of the people are pilots and must occupy the first two seats?

3) From the letters of the word "HEPTAGON", how many three-letter arrangements can be formed if the first letter must be H, one of the other letters must be T, and no letter can be used more than once in any arrangement?

4) How many numbers greater than 400 but less than 10,000 can be formed using the digits 0, 1, 2, 3, 4, and 5 if no digit may be used more than once in any number?

5) If a set of 2x consecutive numbers has y even numbers and the first number in the set is 1, which of the following must be the largest odd number in the set?

y-1
y
2y-1
2y
y+1












Solutions :

1. 7/15,

Two ways. 2 blue marbles or 2 green marbles.

Total probability = P(1 Blue Marble)*P(2nd Blue marble)

P(1 Blue marble) = 4/6
P(2nd Blue Marble) = 3/5

P(2 Blue marbles) = P(1 Blue marble) * P(2nd Blue marble) = 12/30

P(1Green Marble) = 2/6
P(2nd Green Marble) = 1/5

P(2 Green Marbles) = 2/30

Total probability = 12/30 + 2/30 = 7/15

2) The answer is 2 * 24 = 48.. Figure it out.

3) The answer is 12.

1 * 1 * 6 = 6

1 * 6 * 1 = 6

6+6 = 12

4) The answer is 340 = (2*5*4) + (5*5*4*3)

5) The answer is 2y-1 take an example x = 3 and try to figure it out.