Question

A binomial experiment with probability of success p=0.84 and n=7 trials is conducted. What is the probability that the experiment results in 6 or more successes?Do not round your intermediate computations, and round your answer to three decimal places.

Answer 1

Given

p = 0.84

n = 7

x = 6 or more successes

The probability is given by:

$P=C_n^x\cdot p^x\cdot(1-p)^{n-x}$

Then, substitute the values:

$P=(\frac{7\cdot6\cdot5\cdot4\cdot3\cdot2}{1\cdot2\cdot3\cdot4\cdot5\cdot6})\cdot0.84^6\cdot(1-0.84)^{7-6}$

Simplify:

$P=(7)\cdot0.84^6\cdot0.16^1=0.3934$

Round three decimal places is 0.393.

Answer: the probability is 0.393