A fraction x/y is formed by randomly choosing integers for x and y such that 1 ≤ x ≤ 10

M4maths Previous Puzzles

01 Apr 2022 Probability

A fraction x/y is formed by randomly choosing integers for x and y such that
1 ≤ x ≤ 10
1 ≤ y ≤ 7
What is the chance that the fraction is less than 1/2 ?

OPtion

1) 1/14
2) 4/35
3) 1/7
4) 3/35
5) 9/70
6) 2/35
7) 1/5
8) 6/35
9) 11/70
10) None of these

Solution

Possible fractions x/y are 1/1, 1/2, ...., 10/7 => Total Outcomes=10*7=70
For x=1, Fraction x/y < 1/2 are 1/3, 1/4, 1/5, 1/6, 1/7, Total=5
For x=2, Fractions x/y < 1/2 are 2/5, 2/6, 2/7, Total=3
For x=3, Fractions x/y < 1/2 is 3/7, Total=1
Similarly no values of fractions possible for x > 3
Total favorable outcomes=5+3+1=9
Hence, chance or probability that fraction < 1/2 = 9/70

Correct Option: 5 Best Solution (6)

G.S.Kantharao   2 years AGO

Sample space 70
Required out comes=1/7,2/7,3/7,1/6,2/6,
1/5,2/5,1/4,1/3=9
So probability =9/70
My option is 5👈

Like? Yes (6) | No   

Dr.Dipin Singh   2 years AGO

Out of 70 possible combinations, acceptable 9 combinations are
(1,3), (1,4), (1,5), (1,6), (1,7), (2,5),(2,6), (2,7), (3,7).
So chance = 9/70

Like? Yes (4) | No   

Mayank Kandoi   2 years AGO

Less than 1/2 = 1/3, 1/4, 1/5, 1/6, 1/7
Less than 2/4 = 2/5, 2/6, 2/7
Less than 3/6 = 3/7

Total outcomes = 10*7 = 70
Favourable outcomes = 5+3+1 = 9
Probability = 9/70

Option 5

Like? Yes (4) | No (1)  

RAMADURAI NATESAN   2 years AGO

Total events = 10*7 = 70.
Favourable are 1/3 to 1/7, 2/5 to 2/7 ,and 3/7 = 9.
P = 9/70

Like? Yes (2) | No   

Varun   2 years AGO

Less than 1/2
Means
Numerator 1 has chances with denominator 3,4,5,6,7
2 with 5,6,7
3 with 7
So 9 possibilities of total 10*7

Like? Yes (2) | No   

Pargat Pal Singh   2 years AGO

Total possible combinations= 10*7=70
Favourable combinations are 9 which are listed below:-
x...y
1...3,4,5,6,7 means 5 combinations
2.... 5,6,7 means 3 combinations
3... 7.... only 1 combination
Probability that fraction x/y is less than 1/2 = 9/70

Like? Yes (3) | No (2)