A problem by aman tiwari

Level pending

4 whole numbers are taken at random and multiplied together. The probability that the last digit in the product is 1 , 3 , 7 , 9 1,3,7, 9 can be expressed as a b \frac { a}{b } where a and b are co-prime positive integers then find a+b.


The answer is 641.

Aman Tiwari by aman tiwari , 22, India

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

2 solutions

Daniel Chiu
Dec 22, 2013

The last digit will be 1, 3, 7, or 9 if and only if none of the numbers is divisible by 2 or 5. The probability of this is ( 2 5 ) 4 = 16 625 \left(\dfrac{2}{5}\right)^4=\dfrac{16}{625} The answer is 16 + 625 = 641 16+625=\boxed{641} .

2 Helpful 0 Interesting 0 Brilliant 0 Confused

simple technique

pandiya rajan - 7 years, 5 months ago
Anubhav Singh
Dec 22, 2013

Each of the digits 0,1,...,9 occur in 4 ways in the units digit (since we are multiplying 4 whole numbers). so, the total no. of ways = 10^4

Each of the digits 1,3,7,9 can occur in 4^4 ways.

So the prob. = 4^4/10^4=16/625 16+625=641

0 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...