Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

Pages: **1**

**genericname****Member**- Registered: 2012-05-16
- Posts: 52

Hi, how do I prove that the sum of all the probabilities is equal to 1 for this problem?

*Flip a coin until heads show, assume that the probability of heads on one flip is 4/5. We define a random variable X = the number of flips.*

*a) What are the possible values of X?b) Find the probability distribution for X: give the first four values and then find a general formula for the probability that X = nc) Prove that the sum of all probabilities is 1 using the formula for the sum of a geometric series.*

My answers:

a) X=1,2,3,...,n

b)

p(1) = 4/5

p(2) = 4/25

p(3) = 4/125

p(n) = ((1/5)^n-1) * (4/5)

Offline

**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,525

hi genericname

The series could continue for ever so you need the sum to infinity of a geometric series.

Here 'a' is the first term 4/5 and r is 1/5

http://www.mathsisfun.com/algebra/seque … etric.html

Bob

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Offline

**genericname****Member**- Registered: 2012-05-16
- Posts: 52

Thank you, bob.

Offline

Pages: **1**