search
Log In
15 votes
4.7k views

The probability that a $k$-digit number does NOT contain the digits $0, 5,$ or $9$ is

  1. $0.3^{k}$
  2. $0.6^{k}$
  3. $0.7^{k}$
  4. $0.9^{k}$
in Quantitative Aptitude
edited by
4.7k views
7
Here we're approximating $\frac{7}{9}*\frac{7}{10}*\frac{7}{10}*\frac{7}{10}*\frac{7}{10}....$k times

and considering it $(\frac{7}{10})^{k}$

7 Answers

24 votes
 
Best answer

Total possibilities =$(10)^{k},$ because every digit has $10$ options from $0\;to\; 9.$
 

Possibility of not containing any digit $0, 5, 9 = (7)^{k},$ now every digit has $7$ options.

Asked probability =$\dfrac{(7)^{k}}{(10)^{k}} = (0.7)^k$
 

So C is the answer.

1 flag:
✌ Edit necessary (prithatiti “if 0 comes in first place it would no longer be a K digit number, but, a (k-1) digit number.”)

edited by
14
Hello,

This is obviously incorrect because you consider 10^k total possibilities. That implies that the Most Significant digit can also have any one of 0-9 digit. But, if 0 comes in first place it would no longer be a K digit number, but, a k-1 digit number.
14 votes

so C is the ans.

10 votes

if k=1  p=.7

if k=2  p=.7 x.7 =0.7

in general 0.7k ans is C

6 votes
Probability of digits containing (0, 3 or 5) if we consider a 'k' digit number is of type base 10 = (3/10) ^k

Hence,  p(not containing 0, 3 or 5)=(7/10)^k
6 votes

let p be probability that an ith place in a number  contains digits 0,3 or 5.

then p=3/10

 ~p = 7/10

therefore, probability that a k digit number doesn't contain digits 0,3 or 5 = (~p)(~p)................k times = (7/10)k

                                                                          

5 votes
0.7^k

When digit is one digit number we will have 7 possibility.
0 votes

Probablity=   required outcomes total outcomes

No of ways to form k-digits with no 0, 5, 9 (with repetitions allowed) = 7^k

Total no of ways to for k-digit number( with repetitions allowed)= 9.(10^k-1)

hence probablity=   7^k / 9.(10^k-1)  == 1.11(0.7^k)  similar to option C  

ago
Answer:

Related questions

20 votes
3 answers
1
5.2k views
A contour line joins locations having the same height above the mean sea level. The following is a contour plot of a geographical region. Contour lines are shown at $25$ m intervals in this plot. If in a flood, the water level rises to $525$ m, which of the villages $P, Q, R, S, T$ get submerged? $P, Q$ $P, Q, T$ $R, S, T$ $Q, R, S$
asked Feb 14, 2017 in Quantitative Aptitude Arjun 5.2k views
31 votes
4 answers
2
5k views
The expression $\large \frac{(x+y) - |x-y|}{2}$ is equal to : The maximum of $x$ and $y$ The minimum of $x$ and $y$ $1$ None of the above
asked Feb 14, 2017 in Quantitative Aptitude Arjun 5k views
11 votes
4 answers
3
28 votes
6 answers
4
6.3k views
Arun, Gulab, Neel and Shweta must choose one shirt each from a pile of four shirts coloured red, pink, blue and white respectively. Arun dislikes the colour red and Shweta dislikes the colour white. Gulab and Neel like all the colours. In how many different ways can they choose the shirts so that no one has a shirt with a colour he or she dislikes? $21$ $18$ $16$ $14$
asked Feb 14, 2017 in Quantitative Aptitude Arjun 6.3k views
...