Question

the following box contains 9 letters shown. The letters are drawn one by one without replacement and the result are recorded in order.
find the probabilty of the outcome Professor

Answer 1

these are 8 independent events 
P(P) = 1/9 
P(r )= 2/8
P(o) = 2/7   and so on until  only r is left  
These probabilities are multiplied together to give the  resulting  p(Professor)

So it will be 1/9 * 1/4 * 2/7* 1/6 * 1/5*1/2*1/3 * 1/2  = 2/ 90,720 = 1/45,360

Answer 2

The probability of the outcome is "$\frac{1}{45360}$".

According to the given question, we have eight independent events such as:

• $P(P)=\frac{1}{9}$
• $P(R) = \frac{2}{8}$  $=\frac{1}{4}$
• $P(O) = \frac{2}{7}$
• $P(F) = \frac{1}{6}$
• $P(E) = \frac{1}{5}$
• $P(S) = \frac{1}{2}$
• $P(S) = \frac{1}{3}$
• $P(O)=\frac{1}{2}$

hence,

The Probability will be:

→  $P(Professor) = \frac{1}{9}\times \frac{1}{4}\times \frac{2}{7}\times \frac{1}{6}\times \frac{1}{5}\times \frac{1}{2}\times \frac{1}{3}\times \frac{1}{2}$

                           $=\frac{2}{90720}$

                           $=\frac{1}{45360}$

Thus the above is the appropriate solution.

Learn more about the probability here:

https://brainly.com/question/11234923