You are absolutely correct in your approach. However there seems to be a Typo error on the highlighted part above which should be 24/25


To Answer such question in just Two step you may consider taking Unfavorable case and calculate the favorable at second step

e.g. Probability of him not finding the correct Number in two steps = (24/25)*(23/24) = (23/25)

i.e. Probability of him finding the correct Number in two steps = 1- (23/25) = (2/25) which is same as 50/625
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I think it is 1/25 (Correct in first attempt) + 24/25*1/24 (Correct in 2nd Attempt, it is 1/24 coz he wont repeat the wrong number again.) = 2/25 = 50/625 (Answer E)

I have a question in this,
We have a pool of 5 numbers to choose from out of which we have to select 1.
So, prob of getting correct is 1/5.
which means probability of not correct is 4/5.
So, getting wrong at both places is 4/5 * 4/5 = 16/25.

Therefore getting right at both places is 1 - 16/25 = 9/25.

Can someone tell me where I am going wrong.

-Jack

its E. 50/625 = 2/25

the telephone number is: xxx-xxxxx-ab
we need to find the digits ab:
0, 1, 2, 5, and 7 cannot be in digits ab.
remaining integers 3, 4, 6, 8, and 9 can be chosen for ab.
no of ways the integers can be put in place of ab = 5x5 = 25

prob = 1/25 + 1/25 = 2/25. which is E.

I tried to solve this question in following manner:

Last 2 digit can be chosen out of 3 4 6 8 9
means 5x5 = 25 Numbers can be constructed.

Case 1: Bob able to dial the number in first attempt : 1/25
Case 2: Bob able to dial the number in second attempt :

24/25 x 1/24 = 1/25

case 1 + case 2 = 2/25 which is same as 50/625.

I have seen someone solved second case as 24/25 x 1/25 which is not right.
bcz in second attempt bob will have only 24 choices not 25.
thats why they got 49/625 or approx answer.

The total number of possibilities for the phone numbers is 25,

Therefore the probability of him getting on the firs try is 1/25

Here's where I differ from other posters: I would say that the probability of him getting it right on the second try would be:

(24/25)(1/24)

This is because the probability of him getting it wrong on the first try is 24/24, because there are 24 wrong answers and 1 right one. After that, however, he's already eliminated one possible wrong answer by trying and failing, so the total number of possibilities is now 24. That means he has a 1/24 chance of getting it right after trying one and failing.

This makes the total probability 1/25+1/25, which is exactly 50/625
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Answer should be (E)

5 numbers in each of the last two positions
==> total of 25 2-digit numbers
==> probability of getting it right in one guess = 1/25

Total Probability = P(get it right the first try) + P(get it right the second try)
= 1/25 + [24/25 * 1/25]
= 49/625, closest to (E)
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so Bob is given 2 opportunities to decipher the remaining 2 digits of the code, for this task he has 5 digits to choose from.

IMPORTANT notes to bear in mind before calculation:
- picking a number for place 9 is independent from picking the number for place 10 - i.e. digits can repeat
- if Bob wastes his 1st opportunity he will have better chances to pick the right combination during his second attempt - because by that time he has already proved that one combination is invalid.

So we have all the info needed to do simple calculation:

(1) \(\frac{1}{5}\)*\(\frac{1}{5}\) = \(\frac{1}{25}\) - this is the independent event that he would win on first attempt

OR

(2.1) \(\frac{4}{5}\)*\(\frac{4}{5} = [m]\frac{16}{25}\) - he fails to choose correctly on first attempt because he picks either of the 4 wrong digits for the both places

(2.2) \(\frac{1}{4}\)*\(\frac{1}{4}\)=\(\frac{1}{16}\) - he finally chooses the correct digit out of the remaining 4 for each place independently!

AND

(2.3) Multiply the above two iterations to complete the chances for the second scenario: \(\frac{16}{25}\)*\(\frac{1}{16}\)=\(\frac{1}{25}\)

(3) Sum up \(\frac{1}{25}\)+\(\frac{1}{25}\)=\(\frac{2}{25}\)=\(\frac{50}{625}\)

Good question +1

Probability of at least in 2 attempts = Prob in 1 attempt + Prob of Not 1 atempt * Prob of 2nd attempt

Therefore probability of 1 attempt = 1/25

Now this is where the problem gets tricky

Prob of not 1 could be

He found 1
OR He found the other
OR He found neither

So we have 3 scenarios that we'll need to add up

1st scenario: 1/5^3 * 4/5
2nd scenario: 1/5^3 * 4/5
3rd scenario: 4/5^2 * 1/5^2

Now adding all the scenarios = 24/625

Adding 1st and 2nd grand scenario = 1/25 + 24 /625 = 49 / 625.

The closest answer choice is E, cause the problem says approximately

Hope its clear
J

Whats wrong with my method..Can you please elaborate?..Wasn't able to catch you here

I mean to imply that he is not taking a note of the numbers hit earlier and is just going about randomly..as nothing has been mentioned
Anyways this is trivial and GMAC will be more specific..Skip it