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You are watching: If i roll a dice 6 times We are asked to discover the probability that rolling specifically 1 six once rolling a conventional die 6 times.

This is a binomial experiment: there room a fixed number of trials (6), over there are just two outcomes (a 6 or no a 6), the outcomes room independent and the probability...

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We room asked to uncover the probability of rolling exactly 1 six as soon as rolling a conventional die 6 times.

This is a binomial experiment: there room a fixed number of trials (6), there are just two outcomes (a 6 or not a 6), the outcomes space independent and also the probability remains the very same for every trial.

The formula is `(,)p^xq^(n-x) ` whereby `(,) ` is the number of combinations of n objects take away x at a time, ns is the probability the a success, and also q is the match of ns (q=1-p). Here n=6, p=1/6, q=5/6, and also x=1:

`(<6>,<1>)(1/6)^1(5/6)^5=(5/6)^5=3125/7776~~.402 `

Thus P(x=1) is 3125/7776 or around .402

We could likewise get this from first principles:

There are 6 rolls. If just 1 is a 6, climate there is 1 six with probability 1/6, and 5 various other numbers each through probability 5/6. The 6 can take place in any kind of of the six locations so we have actually `6*(1/6)^1*(5/6)^5 ` as above.

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