For each of the problems below, define the sample space S. State whether S is fi
ID: 3221118 • Letter: F
Question
For each of the problems below, define the sample space S. State whether S is finite, countably infinite, or uncountable infinite. If S is finite, calculate |S| (the number of elements in the set S).
a. Toss a coin 5 times and count the number of heads.
b. Toss a coin until the 1st heads appear and count the number of tosses of tails that occur before this happens.
c. Roll four six-sided dice and compute their sum.
d. Roll two six-sided dice and compute their product.
e. Measure the number of unique US customers (rounded to integer millions) that visit Amazon.com Web site in any given 24-hour period. Unique here means that if a person visits the site more than once during the time period, they are only counted once and not multiple times. In 2016, the US population is estimated to be 324 million
Explanation / Answer
a. Toss a coin 5 times and count number of heads.
Sample space : Number of heads :Sample Sapce S :(01,2,3,4,5) Sample space is finite. Number of elements in the sample space |S|= 6;
b. Toss a coin until first head appears and count the number of tosses of tails that occur bfore this happens.
Sample space : Number of tails occur before a head occur. Sample Space :(01,2,3,4,5,........): (first toss head appear, in the first toss tail and second toss head appear, .....) sample size is countbly infinite.
c. Roll a four six sided dice; Compute their sum.
Sample space : sum of the four dice that are rolled. The Sample Space S:( 4,5,.......24): ((1,1,1,1) ; (1,1,1,2) ......(6,6,6,6)). S is Countbly finite. Number of elements in the set(24-4+1=) |S|= 21
d. Roll two-sided dice and compute their product.
Sample space - Product of the number that appear on the two dice. Sample Sapce : (1,2,3,4,...36) :( (1,1);(1,2)......(6,6) ; Number of elements in the set:((36-1+1): |S|:=36
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.