Binomial Distribution
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The probability of rolling a single 2 on a standard six-sided die is 1/6, as there are six possible outcomes and they are equally likely. The probability of rolling two 2s in a row is 1/36, which is calculated by taking the probability of the first roll being a 2 (1/6) and multiplying it by the probability of the second roll also being a 2 (1/6), as the two rolls are independent events. This use of multiplying the individual probabilities to determine the probability of multiple independent events follows the binomial distribution formula.
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Binomial Distribution
- 2. Rolling a two Given one throw of a die, what is the probability of throwing a 2? Since there are six equally probable outcomes the probability of throwing a 2 is just p=1/6
- 3. Rolling a two twice? What is the probability of throwing two 2's in a row? The combined probability of two independent events is just the product of the probabilities of the two single events =P²=1/6·1/6=1/36 The use of binomial distribution to get this result take the form F b (x)= n!px(1-p)ᵑx fb(x)= 2(1/6)²=1/36 x!(n-x)! 2!