Question

Q3.Give an example a box contain (0.75x5H) Envelops of which (0.5x5H) contain $100 in cash. (0.10x5H) contain $25 in cash rest of the envelops contain $10.

H=7
1. Construct a sample space for the different amount of money.
2. Assign the probabilities to the each sample point.
3. Find the probability that the first envelop purchased contain less than $100.

Answer 1

It is given that H = 7.

There are a total of  
Of these, contain $1000.
contains $25 .
The rest are $10.
That is, contains $100 .

• Sample Space
  The sample space for different amounts of money is: {$100, $25, $10}
  
• Probabilities of each sample point:
  
  
  
  
  Let X be the random variable denoting the amount present in the first envelope chosen.
  Hence, the probability distribution is given by:
  
  
  
• Here, we are to find :
  
  
  
  
  
  

N.B. The validity of the statement of 26.25 envelopes is not known. Maybe 0.75 parts of one envelope is torn off and thrown away or something. Calculations are done on the basis of the information provided.

I hope this clarifies your doubt. If you're satisfied with the solution, hit the Like button. For further clarification, comment below. Thank You. :)