Question

List the elements of the sample space defined by experiment. 1. a) Roll a single die and then toss a coin c) Toss two coins. 2. Use the counting principle to determine the number of elements in the sample space. Two digits are selected: a) With replacement from the digits 1, 2, 3, and 4 b) Without replacement from the digits 1, 2, 3, and 4. 3. Two-digit natural numbers are formed, with replacement, from the digits 0 through 9.How many numbers are greater than 67? 4. A gold, a silver, and a bronze medal are awarded in an Olympic event. In how m ways can the medals be awarded for a 200-meter sprint in which there are 9 runners? 5. A professor gives his students 7 essay questions to prepare for an exam. Only 5 of the questions will actually appear on the exam. How many different exams are possible?

Answer 1

1) a)Roll a die and toss a coin

For coin there are two outcomes - Head or Tail

For die there are 6 outcomes - 1,2,3,4,5,6

So total elements sample space = 6*2 = 12

Sample space :  H 1 , H 2 , H 3 , H 4 , H 5 , H 6 , T 1 , T 2 , T 3 , T 4 , T 5 , T 6.

c) Two coins

So total elements sample space = 2*2 = 4

sample space : HT, HH , TT , TH

2) a) with replacement

2 digits from 4

So the first digit has 4 choices

And the second digit also has 4 choices

Total elements = 4*4 = 16

b) without replacement

2 digits from 4

So the first digit has 4 choices

And the second digit has 3 choices

Total elements = 4*3 = 12

Sorry, but Chegg policy for multiple asked question/subparts is to only answer first four. So I have answered the first four, still, i will give you the answers and hint for the next 3 questions.

3) Greater than 67

Case 1 greater than 70

So the first digit has 3 choices ( 7,8,9 )

And the second digit has all 10 choices

Total numbers : 10*3 = 30

and we left 68 and 69 so 30 +2 = 32

Answer = 32

4) 9 runners 3 medals

So Total ways = ⁹P₃ = 9*8*7 = 504

5) 7 question to select 5

So total ways = ⁷C₅ = 21

If any doubt please feel free to ask through the comments section. Thank You