Question - Calculating Number of Trials in Binomial Test with Probability 1/2
Solution:
The question provided in the image asks to find the value of $$ n $$ in a binomial test where $$ p = 1/2 $$, $$ p \cdot n = 35 $$, and $$ q \cdot n = 35 $$ as well. Here, $$ p $$ is the probability of success on a single trial, $$ q $$ is the probability of failure on a single trial, and $$ n $$ is the number of trials.Since $$ p = 1/2 $$, this means that $$ q $$, the probability of failure, must also be equal to $$ 1/2 $$ since $$ p + q = 1 $$.Given $$ p \cdot n = 35 $$, and we know $$ p = 1/2 $$, we can solve for $$ n $$ as follows:\[ 1/2 \cdot n = 35 \]Now, to find $$ n $$, we multiply both sides of the equation by 2:\[ n = 2 \cdot 35 \]\[ n = 70 \]Therefore, $$ n $$, the number of trials, is 70.
CamTutor
In regards to math, we are professionals.
Get In Touch
Email: camtutor.ai@gmail.com