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Probability: Hopelessly Romantic & Number of Paswords

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1. About 8% of the populaiton are hopelessly romantic. If two people are randomly selected, what is the probability both are hopelessly romantic? What is the probability at least one is hopelessly romantic?

2. A password consist of 1 letter and followed by a six diget number.

How many passwords are possible if not restrictions?
How many passwords are prossible if none of the letters or digits can be repeated?

What is the possibility of guessing the password in one trial if there are no restrictions?

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Solution Summary

The solution provides step by step method for the calculation of probabilities. Formula for the calculation and Interpretations of the results are also included.

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Probability questions
1. About 8% of the population are hopelessly romantic. If two people are randomly selected what is the probability both are hopelessly romantic? What is the probability at least one is hopelessly romantic
Answers
Let A be the event of selecting a hopelessly romantic person and B be that of another hopelessly romantic person. Then P (A) = P (B) = 0.08, P (Ac) = P (Bc) = 1 - 0.08 = 0.92
P (both are hopelessly romantic) = P (A ∩ B)
= P (A) * P (B) (Since both the events are independent)
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