Q1. A number of 4 different digits is formed by using 1, 2, 3, 4, 5, 6, 7. Find
the probability that it is divisible by 5.
Q2.A bag contains 5 red, 4 blue and an unknown number of m green balls.Two balls are drawn. If probability of both being green is 1/7 find m.
(1)
The total four digit numbers that can be formed by the digits 1, 2, 3, 4, 5, 6, 7 are 7 × 6 × 5 × 4 = 840
Total four digit numbers that can be formed by the digits which is divisible by 5 are:
For the number to be divisible by 5, the last digit must be 5.
So, the number of such numbers are 6 × 5 × 4 = 120. (it is given in the question that the number should be formed by different digits)
The probability that it is divisible by 5 =
(2)
The number of red balls = 5, the number of blue balls = 4, the number of green balls = m
Total number of balls = 5 + 4 + m = 9 + m
Since two balls are drawn, the number of ways in which both the balls being drawn are green =
Total number of ways in which two balls can be drawn are
Probability =
since the number of balls can never be negative,
So, m = – 2 is rejected.
Hence, m = 6
Thus, the number of green balls = 6.