Logo
Home Study Material Contact Search
AI Chat FREE
  1. mathematics
  2. basic math
  3. a fair coin is flipped until a head appears. let t

A fair coin is flipped until a head appears. Let the number of flips required be...

60.1K

Verified Solution

Question

Basic Math

A fair coin is flipped until a head appears. Let the number offlips required be denoted N (the head appears on the ,\1th flip).Assu1ne the flips are independent. Let the o utcon1es be denoted byk fork= 1,2,3, . ... The event {N = k} 1neans exactly k flips arerequired. The event {,v;;, k} n1eans at least k flips arerequired.

a. How n1any o utcon1es are there?

b. What is Pr[N = k] (i.e., the probability of a sequence of k -1 tails followed by a heads)? (Hint: write a gene ral expressionfor Pr[N = k] for any k = 1,2,3, .. . )

c. Show the probabilities sum to l (i.e., I:f: 1 Pr[,v = k] =1).

d. What is Pr [ N ;;, I] for all I;;: l?

e. What is Pr[N s /] for all I;;: l?

f. Do the answers to tl1e previous two parts sum to l? Shouldthey?

Answer & Explanation Solved by verified expert
4.2 Ratings (786 Votes)
    See Answer
Get Answers to Unlimited Questions

Join us to gain access to millions of questions and expert answers. Enjoy exclusive benefits tailored just for you!

Membership Benefits:
  • Unlimited Question Access with detailed Answers
  • Zin AI - 3 Million Words
  • 10 Dall-E 3 Images
  • 20 Plot Generations
  • Conversation with Dialogue Memory
  • No Ads, Ever!
  • Access to Our Best AI Platform: Flex AI - Your personal assistant for all your inquiries!
Become a Member

Other questions asked by students

Biology
1.2K views

Give a general description of the light and dark reactions of photosynthesis. Light – light energy...

Chemistry
1.2K views

What is the pH at the equivalence point in the titration of a 23.0 mL sample...

Basic Math
1.2K views

Name the corresponding sides and the corresponding angies of the following pair of similar triangles.

Basic Math
1.2K views

The salaries of 10 employees of a small company are listed. Complete parts (a) through...

Calculus
1.2K views

ystem by the addition method y 6 6 y Ques correct choice below and if...

Algebra
1.2K views

6 Find the axis of symmetry and vertex algebraically graph the function represented by f...

Algebra
1.2K views

Simplify the expression xy 4xy5 x y 5 4xy 5 Simplify your answer

Accounting
1.2K views

Case Study In July 2016, Josh Gavidia and Rae Dineda, co-owners of Style Inc. (Style),...

Accounting
1.2K views

Wilhelm Company collected $7,200 in May of 2020 for 4 months of service which would...

Finance
1.2K views

eft 0:18:51 ition 1 yet wered arked out of DO Burj Khalifa Agrotech has collection...

Accounting
1.2K views

Coy and Matt are equal partners in the Matcoy Partnership. Each partner has a basis...

Accounting
1.2K views

Lamar Corporation purchased land for $190,000. Later in the year the company sold land with...