Lia D.

asked • 11/26/21# help needed. thank you!

- (Question not related to a deck of 52 cards.) You have 5 blue cards, 4 red, and 6 green in a box. If you draw two cards from the box with replacements, find P(Blue and Green).
- Two six sided die are rolled. What is the probability that the sum will be less than 10?
- A group consists of 3 people. If 11 people are able to be in a group, how many different groups can be made?

## 2 Answers By Expert Tutors

Raymond B. answered • 11/28/21

Math, microeconomics or criminal justice

4 Red, 5 Blue, 6 Green, out of 52 cards total

P(B) = 5/52, P(G) = 6/52 = 3/26

P(B&G) = P(B)xP(G) + P(G)xP(B) = 2P(B)xP(G) = 2(5/52)(3/26) = 30/(52)(26) = 15/52(13) = 15/676 = about 2.2%

2 one way 1&1

3 two ways 2&1, 1&2

4 three ways 3&1, 1&3, 2&2

5 four ways

6 five ways

7 six ways

8 five ways

9 four ways

10 three ways 6&4, 4&6, 5&5

11 two ways 5&6, 6&5

12 one way 6&6

total 36 ways

less than 10 happens in 30 ways

P(<10) = P(2,3,4,5,6,7,8 or 9) = 1-Pr(10,11,or 12) = 1 -6/36 = 30/36 = 5/6 = about 83.3%

11C3 = 11!/3!8! = 11(10)(9)/3(2)(1) =11(5)(3) = 161 combinations

if order matters within each group then

11P3 = 11/8! = 11x10x9 = 990 permutations

for combinations ABC, ACB, BAC, BCA, CAB, CBA are all counted as just one group

for permutations they count as 6 different groups

#1 There are 2 possible outcomes to meet the criteria: BG and GB. Write the probability of each, and since they are independent events, add.

#2 Write a 6 x 6 table with the sum of each row and column at each intersection. Then count the intersections which meet the criteria,

#3 This is a straight application of binomial coefficients.

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Mark M.

What help do you want. Each of these is calculated using standard formulas.11/26/21