MHB Solving Probability w/ Cards: Answers & Explanations

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The discussion focuses on calculating probabilities related to a box of 50 index cards, each labeled with a letter. Users seek clarification on their calculations for the probability of drawing two cards, both being 'A', and the probability of drawing two cards that are not vowels. The initial calculations presented are questioned for accuracy, particularly regarding the total number of non-vowel cards and the need to simplify fractions. The importance of understanding the wording of probability questions is emphasized to avoid confusion. Accurate calculations and simplifications are crucial for correctly solving probability problems.
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I just want to make sure I have these answers right... if they are not can you please explain how to get the right answer. The wording of the question is what gets me confused with probability.
A box contains 50 index cards. One letter is written on each card. There are
5 cards with the letter A
5 cards with the letter E
7 cards with the letter H
10 cards with the letter M
3 cards with the letter S
20 cards with the letter T

If one card is selected, replaced, and a second card selected, determine:

a) p(both A)
I have: 25/2500 = .01

b) p(neither is a vowel)
I have: 70/2500= .028If one card is selected, not replaced, and second card selected, determine:

a) p(both A)
I have: 20/2450= .008163

b) p(neither is a vowel)
I have: 57/2450= .023265Thanks for the help!
 
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CosmoK123456 said:
I just want to make sure I have these answers right... if they are not can you please explain how to get the right answer. The wording of the question is what gets me confused with probability.
A box contains 50 index cards. One letter is written on each card. There are
5 cards with the letter A
5 cards with the letter E
7 cards with the letter H
10 cards with the letter M
3 cards with the letter S
20 cards with the letter T

If one card is selected, replaced, and a second card selected, determine:

a) p(both A)
I have: 25/2500 = .01

b) p(neither is a vowel)
I have: 70/2500= .028

How the heck did you get get that?
There are 40 non-vowels.
 
I would also recommend reducing the fractions before applying the special multiplication rule. Keeping it simple reduces the risk of error. :D
 
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