Board game probability

Probability Level 1

A group of friends is playing a board game.

It is Mike's turn, and he is almost at the finish. Mike will roll a fair six-sided die to determine how many spaces he moves, and then he will flip a coin to determine if he goes forwards or backwards.

Mike needs to move forward at least 4 spaces to win. What is the probability that Mike wins the game on this turn?

Image Credit : Gadini


The answer is 0.25.

Andy Hayes by Andy Hayes , 38, USA

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2 solutions

Andy Hayes
Jun 14, 2016

Let F F represent a forward move and B B represent a backward move. The sample space of this experiment is as follows:

S = { 1 F , 2 F , 3 F , 4 F , 5 F , 6 F , 1 B , 2 B , 3 B , 4 B , 5 B , 6 B } S=\{1F,2F,3F,4F,5F,6F,1B,2B,3B,4B,5B,6B\}

Both the die and the coin are fair, so this sample space is uniform.

Let W W be the event that Mike wins the game. W = { 4 F , 5 F , 6 F } W=\{4F,5F,6F\}

P ( W ) = ∣ W ∣ ∣ S ∣ = 3 12 = 0.25 P(W)=\dfrac{|W|}{|S|}=\dfrac{3}{12}=0.25

The probability that Mike wins the game is 0.25 \boxed{0.25} .

15 Helpful 0 Interesting 1 Brilliant 0 Confused

Is it not 0.5? Because in my view: W = {3F,4F,5F,5B,6F,6B}. Doesn't the question say he needs a number >=4.

Bradley Nkomo - 2 years, 10 months ago

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Exactly, that's what I thought as well

Zimehr Abbasi - 2 years, 4 months ago

The example is not explained correctly. It states that the player need to move 4 spaces, not at least 4 spaces to win.

Adam Winschberg - 1 year, 7 months ago

It states that the player needs to move exactly 4 spaces

Palanichamy D - 1 year, 6 months ago
Rex Holmes
Sep 8, 2016

Mike has to get 4 or more and move forward to win. since their are six sides of a die, the only numbers which are greater then or equal to 4 are 4, 5, and 6 3/6 of then numbers on a die equal 0.5 then he has to flip a coin to see if he goes forward or backward since their are 2 sides of a coin he has a 1/2 chance of going forward assuming it is a fair die 1/2 equal 0.5. 0.5X0.5=0.25

7 Helpful 0 Interesting 0 Brilliant 0 Confused

This problem is quite vague. The "forward or backwards" was not interpreted as sign to me, but rather as going plus one after the roll or minus one. My mistake, but try to make it more clear. I used convolution on this one

Charlie Tian - 4 years ago

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