This discussion is closed.
flyinghorse
Badges: 0
Rep:
?
#1
Report Thread starter 14 years ago
#1
A bag contains three balls - one red, one white, one orange.

A ball is chosen at random and replaced.

If the ball is white, the player receives two counters.

If the ball is orange, the player receives one counter.

If the ball is red, the player receives no counters.

What is the expected number of counters that the player will gain before choosing the red ball for the first time?
0
Jonny W
Badges: 8
Rep:
?
#2
Report 14 years ago
#2
Let X be the number of balls chosen up to and including the first red one. Since X ~ Geometric(1/3), E(X) = 3.

Let C be the number of counters gained from the first X draws.

Then

E(C | X = x) = (3/2)(x - 1)

because, conditional on X = x, each of the first x - 1 balls is independently white (with probability 1/2) or orange (with probability 1/2).

E(C)
= (sum over x) E(C | X = x)P(X = x)
= (sum over x) (3/2)(x - 1)P(X = x)
= (3/2)(E(X) - 1)
= 3
0
X
new posts
Back
to top
Latest
My Feed

See more of what you like on
The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

Personalise

University open days

  • University of Bristol
    Undergraduate Open Afternoon Undergraduate
    Wed, 23 Oct '19
  • University of Exeter
    Undergraduate Open Day - Penryn Campus Undergraduate
    Wed, 23 Oct '19
  • University of Nottingham
    Mini Open Day Undergraduate
    Wed, 23 Oct '19

Have you made up your mind on your five uni choices?

Yes I know where I'm applying (144)
60.25%
No I haven't decided yet (54)
22.59%
Yes but I might change my mind (41)
17.15%

Watched Threads

View All