suppose you flip a coin n times, and the probability of getting heads 15 times is .0148. what's n?

Question

Hero · Answer

@avi8tor are you familiar with the Binomial Probability Formula?

The Binomial Probability Formula:
$$P(x)  = \large\dfrac{n!}{x!(n - x)!}^{p^xq^{(n - x)}}$$

Where 
$x$ represents the number of successes
$n$ represents the number of trials
$p$ represents the probability of success
$q$ represents the probability of failure $\left(\text{In other words  }, q = 1 - p\right)$

In this case
$x$ represents the number of times heads is flipped $(x = 15)$
$n$ represents the total number of times the coin is flipped $\left(\text{What we have to find}\right)$
$p$ represents the probability of flipping heads in one event $ p = \left(\dfrac{1}{2}\right)$
$q$ represents the probability of flipping tails in one event $q = 1 - \left(\dfrac{1}{2}\right) = \dfrac{1}{2}$

Hero · Answer

You can find $n$ by plugging all the values in to the formula and using trial and error for n values. We know this much: $n \ge 15$

Hero · Answer

BTW, $P(x)$ represents the probability of achieving $x$ number of successes out of $n$ events.

Ultrilliam · Answer

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