Register

ISI2018-MMA-17

1,190 views
0 votes
0 votes

There are eight coins, seven of which have the same weight and the other one weighs more. In order to find the coin having more weight, a person randomly chooses two coins and puts one coin on each side of a common balance. If these two coins are found to have the same weight, the person then randomly chooses two more coins from the rest and follows the same method as before. The probability that the coin will be identified at the second draw is

  1. $1/2$
  2. $1/3$
  3. $1/4$
  4. $1/6$
User Avatar

2 Answers

0 votes
0 votes

Key points 

  • There are eight coins, seven of which have the same weight and the other one weighs more.
  •  the coin will be identified at the second draw 

Now how to identified in $2 nd $ draw?

In $1st $ draw , we must drawn $2$ unequal weight coin. Now, pick one coin from rest and put in common balance with any one of $2$ previous coin.

If it is equal weight, another coin of $1 st$ draw has more weight. This is only one possibility for it.

Now, maximum possibility will be $4.$ 

  • Pick $1st$ two coin in common balance and got equal weight
  • Pick next two coin in common balance and got equal weight
  • Pick next two coin in common balance and got equal weight
  • Now, pick only one coin and balance with any prev coin. If it has equal weight, then $8 th$ coin has more weight. Otherwise $7th$ one.

So, probability will be $\frac{1}{4}$

User Avatar
–1 votes
–1 votes
B. 1/3
5C1 . 1C1 / 6C2 = 5/15 = 1/3
User Avatar
Voting & Accepting an answer helps improve the community
← PreviousNext →
← Previous in categoryNext in category →

Related questions

1 votes
1 votes
2 answers
1
akash.dinkar12 asked May 11, 2019
2,148 views
ISI2018-MMA-20
Consider the set of all functions from $\{1, 2, . . . ,m\}$ to $\{1, 2, . . . , n\}$,where $n > m$. If a function is chosen from this set at random, the probability that it will be strictly increasing is $\binom{n}{m}/n^m\\$ $\binom{n}{m}/m^n\\$ $\binom{m+n-1}{m-1}/n^m\\$ $\binom{m+n-1}{m}/m^n$
Consider the set of all functions from $\{1, 2, . . . ,m\}$ to $\{1, 2, . . . , n\}$,where $n m$. If a function is chosen from this set at random, the probability that i...
User Avatar
1 votes
1 votes
4 answers
4
akash.dinkar12 asked May 11, 2019
1,216 views
ISI2018-MMA-28
Consider the following functions $f(x)=\begin{cases} 1, & \text{if } \mid x \mid \leq 1 \\ 0, & \text{if } \mid x \mid >1 \end{cases}.$ ... at $\pm1$ $h_2$ is continuous everywhere and $h_1$ has discontinuity at $\pm2$ $h_1$ has discontinuity at $\pm 2$ and $h_2$ has discontinuity at $\pm1$.
Consider the following functions$f(x)=\begin{cases} 1, & \text{if } \mid x \mid \leq 1 \\ 0, & \text{if } \mid x \mid >1 \end{cases}.$ and $g(x)=\begin{cases} 1, & \te...
User Avatar
Link Copied!