Question

A coin is slightly bent, and as a result the probability of a head is 0.52. Suppose that you toss the coin four times. Use the Binomial formula to find the probability of 3 or more heads

Answer 1

Hi Spor7tdardLamilokab, this particular equation is a binomial probability equation:

P(X) = $( \frac{n}{k})$ * $p^{k}$ *$(1 - p)^{n-k}$

Note that it's not n / k, but rather the notation is n choose k. Brainly software will not allow me to do this, but imagine the n choose k, without the bar, and that the correct notation.
 
Where $(\frac{n}{k})$ equals  $\frac{n!}{k!(n-k)!}$ , where n! is n * (n-1) * (n-2) 8 ... 1

So for your particular equation:

$P(x \geq 3) = (\frac{5}{3}) * 0.52^{3} * (1 - .52)^{5-3}$

You would repeat the above equation for 4 as well and add that to the computation for 3, since you want the probability that you'll get 3 or more heads.

Solving this produces the answer:

P(x$\geq$ 3) = 0.34308352

You can also solve this with a TI 83 or 84.

To do this, the steps are 2ND | VARS (or DISTR) | BINOMPDF| TRIALS | PROBABILITY | X VALUE

Doing this for 3 and 4 produces the same result:

binompdf(4, 0.52, 3) + binompdf(4, 0.52, 4) = 0.34308352