2) This is the problem that gave rise to the mathematical topic known as probabi

Question

2) This is the problem that gave rise to the mathematical topic known as probability: Two players each put money into the pot. Player A was to toss a single die in the attempt to throw a six. This player had 8 tries in which to do this. If player A succeeded in throwing a six, he would win the pot. If he failed, player B would win the pot. Unfortunately, the game was forced to come to a premature end (the police arrived?) after only three unsuccessful tosses. The dispute was how the pot should be divided under these unusual circumstances. Find the probability that player A would have won. That is, find the probability that player A would have thrown a six in his remaining five tosses.

Explanation / Answer

Solution:

Binomial probability distribution

Formula:

P(k out of n )= n!*pk * qn-k / k! *(n - k)!

n = 5

p = 1 / 6 = 0.1666

q = 1 - p = 1 - 0.1666 = 0.8334

p( x = 1 ) = 5!*0.16661 * 0.83345-1 / 1! *(5 - 1)!

= 0.4081

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