Binomial distribution, odds and probabilities. Johnny is playing Pok´emon cards

Question

Binomial distribution, odds and probabilities. Johnny is playing Pok´emon cards with his friend. It’s Johnny’s turn, and he decides to use Marowak. The card says the following

Flip a coin four times. The amount of damage done to your opponent’s Pok´emon is the number of heads times 40.

What are the odds that Marowak will do at least 120 damage to the opponent? One approach to answer this question is to use the Binomial distribution to compute the probability of doing at least 120 damage and then convert from probability to odds. You can take another approach if you prefer. In any case, assume that the coin is fair, i.e. the probability of getting heads on any particular toss is 1/2.

Explanation / Answer

assumption is that the coin is fair . so P[Head]=1/2

let X be the number denoting the number of heads when the coin is flipped 4 times

so X~Bin(4,0.5)

Y denotes the damage. so Y=X*40

we need to find P[Y>=120]

now P[Y>=120]=P[X*40>=120]=P[X>=3]=P[X=3]+P[X=4]=4C30.54+4C40.54=5/16

hence odds that Marowak will do at least 120 damage to the opponent is 5/(16-5)=5/11 [answer]

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