Summer fun 17

There are 90 possibilities for the answer,so the chance of him getting it wrong at the first three times is $\dfrac{89}{90}\times\dfrac{88}{89}\times\dfrac{87}{88}=\dfrac{29}{30}$ .

So the chance to get it right is $1-\dfrac{29}{30}=\dfrac1{30}\approx0.03=3\%$

the probability of correct answer being in the set of 3 numbers that he randomly chooses out of all the 90 possibilities is 3/90. i.e. 0.033

As they asked for total probability Find probability of each guess differently and add them as they are held together at same time (1/90+1/89+1/88) 100= 0.0337 100 =3%

Every person solving problems on brilliant.org has been this user once

Split it up, let the probability he guess at the $x$ -th time is correct to be $P(x)$ for all $1\leq x\leq 3$ , then we have $P(1)=\dfrac1{90}$ $P(2)=\dfrac{89}{90}\times\dfrac{1}{89}=\dfrac{1}{90}$ $P(3)=\dfrac{89}{90}\times\dfrac{88}{89}\times\dfrac1{88}=\dfrac1{90}$ There of them have the same probability, that means the probabilities he guess the right answer is the same no matter it is which time (sorry for broken English).

Turn back to the main topic, the probability he guess the right answer will be $\sum_{i=1}^3P(i)=\dfrac1{90}+\dfrac1{90}+\dfrac1{90}=\boxed{\dfrac1{30}}$ which is approximately $\boxed{0.3\%}$ .

The probability of getting the answer right on the first guess is $\frac{1}{90}$ .

The probability of getting the answer right on the second guess is the probability of getting it wrong on the first guess multiplied by the probability of getting it right on the second guess, with the new information that you have. Therefore, it is $\frac{89}{90}\cdot\frac{1}{89}=\frac{1}{90}$ .

Similarly, the probability of getting the answer right on the third guess is the probability of getting it wrong on the first and second guess multiplied by the probability of getting it right on the third guess, with the new information that you have. Therefore, it is $\frac{89}{90}\cdot\frac{88}{89}\cdot\frac{1}{88}=\frac{1}{90}$ .

$\frac{1}{90}+\frac{1}{90}+\frac{1}{90}=\frac{1}{30}=0.0\overline{3}=3.\overline{3}\%\approx3\%$

Here's a brief Julia 0.5.0 snippet showing experimental evidence:

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begin
  f=0;s=0;t=0;dnf=0
  secret=rand(10:99)
  for i in 1:10000000
    range=collect((10:99))
    fn=rand(range) 
    filter!(x->x!=fn,range)
    sn=rand(range)
    filter!(x->x!=sn,range)
    tn=rand(range) 
    if secret == fn
      f += 1
    elseif secret == sn
      s += 1
    elseif secret ==tn
      t += 1
    else
      dnf += 1
    end
  end
  println("Found on the first try: $(f*100/10000000)%")
  println("Found on the second try: $(s*100/10000000)%")
  println("Found on the third try: $(t*100/10000000)%")
  println("Found overall: $((f+s+t)*100/10000000)%")
end

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Found on the first try: 1.11029%
Found on the second try: 1.11764%
Found on the third try: 1.11217%
Found overall: 3.3401%%

EDIT: Original code could guess the same number twice,fixed with updated values.

3/100=3% which is equalivent to 0.03.

3 guesses of 90 possibilities gives 3/90=0.0333=3.33% chances to get it right.

There is 90 possibilities number: 9x10=90 So we have 3 times to guess the answer. 3/90=0.0333333 => 3%

Our number is: xy. x is the first, y the second iteger. 0 can be combinated with 1,2,...,9 (not 0, because we wouldn‘t earn a positive number. 1,2,3,...,9 can be combinated with 0,1,...9 (we would get a positive number). That means we have 1 time 9 possibilities and 9 times 10: 9+10x9=99. First try: 1/99, second try: 1/98 (we tried one possibility), third try: 1/97 —> 1/99+1/98+1/97=0,03(...) —> 3%

There are 90 possibilities for picking the right number. The 3 tries give you a 3/90 which is an approx 3% chance.

I got the answer right but mostly from luck. In my head I thought 99 possible answers, for getting that it will be double digits and not single. I then rounded up to 100. 3 tries out of 100 is 3% of possible answers.

There are 90 possibilities. Each guess has a $\frac{1}{90}$ chance of being correct. They have three chances. Multiply the probability by three and you have a 3 in 90 chance, or 1 in 30, which is approximately equal to a 3% chance

There are 99 - 10 + 1 = 90 positive 2-digit integers. The chance of picking the right number in 3 guesses is 3*(1/90) = 1/30 ~ 3.33/100 ~ 3%.

Intuitively: it shouldn't matter if you go step by step or pick three at once. 3/90 ~3.33%

If you test with a smaller set of numbers (5), and more guesses (4) : 1/5+1/4+1/3+1/2 ~ 128% > 100% you still have one number left so 1/99+1/98... doesn't work.

We know that 2 digit possible positive integers are 90 and he has 3 tries. Therefore the formula for percentage is n/x ×100

.•. 3/90 ×100 = 3.33333333.... % Rounded to nearest integer is 3%

There are 90 possibilities for the first guess, 89 for second and 88 for the third. Sum the chance of getting a right guess for each of the guesses: $\frac{1}{90}$ + $\frac{1}{89}$ + $\frac{1}{88}$ $\approx0.03=3\%$