A die is thrown 6 times. If 'getting an odd number' is a success, what is the probability of at most 5 successes?

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A die is thrown 6 times. If ‘getting an odd number’ is a success, what is the probability of at most 5 successes?

A die is thrown 6 times. If ‘getting an odd number’ is a success, what is the probability of at most 5 successes?

Solution:

Bernoulli trials are known for their repeated tosses of a dice.

Let $x$ be the number of times an odd number was obtained in a six-trial experiment.

Probability of getting at most 5 successes $=\mathrm{P}(\mathrm{X} \leq 5)$

We can also write it as: $1-\mathrm{P}(\mathrm{X}>5)$

$=1-P(X=6)$

$=1-{ }^{6} \mathrm{C}_{6}(1 / 2)^{6}$

$=1-1 / 64$

$=63 / 64$

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