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((1)/(2))^3\cdot((1)/(2))^((6-3))`

The combinations are given by:

`(6!)/((6-3)!\cdot3!)=(6\cdot4\cdot3!)/(3!\cdot3!)=(6\cdot4)/(3\cdot2\cdot1)=(24)/(6)=4`

Then, we have:

`4\cdot((1)/(2))^3\cdot((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%.