Difference between revisions of "1978 AHSME Problems/Problem 19"
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Let's say that we will have <math>3</math> slips for every number not exceeding <math>100</math> but bigger than <math>50.</math> This is to account for the <math>3p</math> probability part. Let's now say that we will only have one slip for each number below or equal to <math>50.</math> The probability(or <math>p</math>) will then be <math>\frac{1}{200}.</math> Now let's have all the squares under <math>50,</math> which are <math>1,4,9,16,25,36,49.</math> The probability for these are <math>\frac{7}{200}.</math> The numbers above <math>50</math> that are squares are <math>64,81,100.</math> We then need to multiply the probability by <math>3</math> so the probability of these are <math>\frac{9}{200}.</math> The answer is <math>\frac{7}{200}+\frac{9}{200}=0.008\implies\boxed{\textbf{(C).}}</math> | Let's say that we will have <math>3</math> slips for every number not exceeding <math>100</math> but bigger than <math>50.</math> This is to account for the <math>3p</math> probability part. Let's now say that we will only have one slip for each number below or equal to <math>50.</math> The probability(or <math>p</math>) will then be <math>\frac{1}{200}.</math> Now let's have all the squares under <math>50,</math> which are <math>1,4,9,16,25,36,49.</math> The probability for these are <math>\frac{7}{200}.</math> The numbers above <math>50</math> that are squares are <math>64,81,100.</math> We then need to multiply the probability by <math>3</math> so the probability of these are <math>\frac{9}{200}.</math> The answer is <math>\frac{7}{200}+\frac{9}{200}=0.008\implies\boxed{\textbf{(C).}}</math> | ||
~volkie thangy | ~volkie thangy | ||
Revision as of 15:18, 18 June 2021
Problem
Solution
Let's say that we will have 
slips for every number not exceeding 
but bigger than 
This is to account for the 
probability part. Let's now say that we will only have one slip for each number below or equal to The probability(or 
) will then be 
Now let's have all the squares under 
which are 
The probability for these are 
The numbers above 
that are squares are 
We then need to multiply the probability by so the probability of these are 
The answer is 
~volkie thangy
