0 In the classic movie \"It\'s a Wonderful Life\", George Bailey and Mary Hatch
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0 In the classic movie "It's a Wonderful Life", George Bailey and Mary Hatch perform the Charleston at the school dance, which is held at the gym. Assume that each step of their dance has them take a step to the left with probability 2/3, and a step to the right with probability 1/3. We'll assume the gym is infinitely wide, and if left to their own devices, the couple would dance forever. Mary and George begin their dance at position x =-3. A prankster, who is jealous that George is dancing with Mary, opens the floor of the gym, which contains a large swimming pool located at x = 0, A diagram of the unfortunate situation is shown, with the dot representing the couple's initial position. What is the probability that Mary and George will eventually fall into the swimming pool?Explanation / Answer
Rolling a single die
1) probability of rolling divisors of 6 :
Since its a single die, the possible outcomes are 1,2,3,4,5,6. All have equal probability(1/6) since its a fair die
Out of these divisors of 6 are 1,2,3,6. So P(divisors of 6) = 1/6*1/6*1/6*1/6 = 1/1296 = 0.0008
2) probability of rolling a multiple of 1: Since all(1,2,3,4,5,6) are multiples of 6 = 1/6*1/6*1/6*1/6*1/6*1/6= 1/46656 = 0.00002
3) probability of rolling an even number : There are 3 even numbers between 1-6 i.e. 2,4,6
Hence probability of rolling an even number = 1/6*1/6*1/6 = 1/216 =0.0046
4) List of all possible outcomes of rolling a single die ={1,2,3,4,5,6}
5) probability of rolling factors of 3 : Factors of 3 are 1,3
Hence probability of rolling factors of 3 = 1/6*1/6 = 1/36 = 0.0278
6) probability of rolling a 3 or smaller : 3 or smaller are 1,2,3. Hence the probability = 1/6*1/6*1/6 = 1/216 = 0.0046
7) probability of rolling a prime number: Prime numbers between 1-6 are 2,3,5 hence probability = 1/6*1/6*1/6=1/216=0.0046
8) probability of rolling factors of 4 : Factors of 4 are 1,2,4 hence the probability = 1/6*1/6*1/6 = 1/216 =0.0046
9) probability of rolling divisors of 30 : Divisors of 30 are 1,2,3,5,6 = 1/6*1/6*1/6*1/6*1/6 = 1/7776 = 0.0001
10) probability of rolling factors of 24: Factors of 24 are 1,2,3,4,6 = 1/6*1/6*1/6*1/6*1/6=1/7776=0.0001
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