Why Do I Need to Multiply Probabilities in a Binomial Distribution?

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SUMMARY

The discussion clarifies the necessity of multiplying probabilities in a binomial distribution, specifically in the context of rolling a die. The correct probability calculation for obtaining five non-fives followed by two fives when rolling a die seven times is expressed as P = (5/6)^5 * (1/6)^2. This formula accounts for the specific sequence of outcomes, emphasizing that (5/6)^5 alone does not represent the complete scenario since it ignores the required two fives in the final rolls.

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kelvin macks
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please refer to the second line of solution, since we only concerned about the probability of getting number (5) , then why can't I just just say P=(5/6)^5 , why should I times =(5/6)^5 with (1/6)^2 ?
 

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(5/6)^5*(1/6)^2 is the probability to get five non-fives followed by two fives, when throwing the die seven times. (5/6)^5 is just the probabability to get non-fives the five first times, regardless of if you get any more fives the two last times.
 

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