Question

Find the probability of exactly threesuccesses in six trials of a binomialexperiment in which the probability ofsuccess is 50%.Round to the nearest tenth of apercent.[ ? ]%

Answer 1

We need to find the probability of exactly three successes in six trials of a binomial experiment. Probability of success 50% (no success is 50%).

To find this probability, we need to use the following formula for Bernoulli Trials (or Binomial Experiment):

$comb\text{(6, 3) }\cdot(\frac{1}{2})^3\cdot(\frac{1}{2})^{(6-3)}$

The combinations are given by:

$\frac{6!}{(6-3)!\cdot3!}=\frac{6\cdot4\cdot3!}{3!\cdot3!}=\frac{6\cdot4}{3\cdot2\cdot1}=\frac{24}{6}=4$

Then, we have:

$4\cdot(\frac{1}{2})^3\cdot(\frac{1}{2})^3=0.0625$

Thus, the probability of exactly three successes in six trials of a binomial experiment (which the probability of success is 50%) is 0.0625.

Rounding to the nearest tenth is about p = 0.1 (1/10) or 10%.