Same topic: 1. Consider all passwords of length 10 made up of numbers, lower-case letters, and upper-case...

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Advance Math

Same topic:
1. Consider all passwords of length 10 made up of numbers,lower-case letters, and upper-case letters (from the Englishalphabet).
a) If you pick such a password at random, what is the likelihoodthat it contains exactly 5 lower-case letters?
b) If you pick such a password at random, what is the likelihoodthat it contains at most 9 lower-case letters?
2. Suppose you’re an ornithologist who specializes in Americancrows (Corvus brachyrhynchos), and you’ve collected data on 100such birds. Each bird was classified by sex (male or female), andby size (large or small).
The counts follow:
• Male, Large: 38,
• Male, Small: 13,
• Female, Large: 23,
• Female, Small: 26.
Based on these numbers, what is the probability that a randomlychosed crow from this group is large?
What is the probability that a crow is large if it is alreadyknown to be male? Is the event of being large independent of theevent of being male?

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1Number of lower case letters 26Number of upper case letters 26Number of numbers 10 0 to 9 Total options for a digit 262610 62Total number of 10 digit passwords we can generate using all theabove 3 aNumber of passwords containing exactly 5 See Answer

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