Question

A) A coin is tossed and a die is rolled. Draw the tree diagram to list out every possible outcome for this sequence of events. How many total outcomes are possible?

B) Elementary students are given an ID card that has a picture of their face followed by a 4 digit code. Assuming repetitions are allowed, how many ID cards are possible?

C) Six balls are numbered: 1, 2, 3, 5, 8, and 13. A ball is selected, its number recorded, and replaced. Find the expected value for the numbers that will occur. (when needed, round to 4 decimal places)

D) If three coins are tossed, construct the probability distribution for the number of heads that will occur. Then, find the mean (expected value) for the number of heads that occur.

Answer 1

A)

Tree diagram for all the possible outcomes

Coin	Dice	Outcomes
	1	(H,1)
	2	(H,2)
Head	3	(H,3)
	4	(H,4)
	5	(H,5)
	6	(H,6)
	1	(T,1)
	2	(T,2)
Tail	3	(T,3)
	4	(T,4)
	5	(T,5)
	6	(T,6)

Total number of possible outcomes =12

B)

__ , __ , __ , __

There are 9 ways to pick the first digit ( 1 through 9)

There are 10 ways to pick the 2nd ,3rd, and 4th digits

So, by Fundamental Counting Principle

Possible number of ID cards= 9*10*10*10= 9000 ways

Hence , there are 9000 ID cards are possible.

C)

X	Probability(p)	X*p
1	1/6	1/6
2	1/6	1/3
3	1/6	1/2
5	1/6	5/6
8	1/6	4/3
13	1/6	13/6
Total		16/3

Now

  

D)

Let

X : Event of getting head

Possible outcome for tossing three coins are { HHH , HHT , HTH , HTT, TTT, THH , THT , TTH }

Number of possible outcome = 8

Number of getting no head = 1 i.e., TTT

Number of getting 1 head = 3 i.e., TTH , THT, HTT

Number of getting 2 head = 3 i.e., THH, HHT, HTH

Number of getting 3 head = 1 i.e., TTT

Probability distribution table

X	p	X*p
0	1/8	0
1	3/8	3/8
2	3/8	3/4
3	1/8	3/8
Total		3/2

= 3/2

= 1.5

The mean (expected value) for the number of heads that occur= 1.5