Answer to Question #120704 in Statistics and Probability for Mahnoor Qazi

Question

A box contains 500 envelopes, of which 75 contain $100 in cash, 150 contain $25, and 275
contain $10. An envelope may be purchased for $25. What is the sample space for the different amounts
of money? Assign probabilities to the sample points and then find the probability that the first envelope
purchased contains less than $100

Answer 1

A box contains 500 envelopes, of which 75 contain $100 in cash, 150 contain $25, and 275 contain $10.

Hence, the sample space for the different amounts of money is

$$S=\{\$100,\$75,\$10\}$$

$$P(\$100\ envelope)={75\over500}=0.15$$

$$P(\$25\ envelope)={150\over500}=0.30$$

$$P(\$10\ envelope)={275\over500}=0.55$$

Among 500 envelopes there are $150+275=425$ envelopes whivh contain less than $100.

The probability that the first envelope purchased contains less than $100 is

$$P(first \ envelope<\$100)={425\over500}=0.85$$