Question

Two numbers are selected randomly from the set s={1,2,3,4,5,6} without replacement one by one the probability that minimum of the two numbers is less than 4 is

Answer 1

The probability that minimum of the two numbers is less than 4 is $\frac{4}{5}$

Explanation:

Given that the two numbers are selected randomly from the set s is given by

$s=\{1,2,3,4,5,6\}$

We need to determine the probability that without replacement one by one the minimum of the two numbers is less than 4.

The total ways is given by

$2! \ ^6C_2$ = $(2\times1)\frac{(6\times5)}{2\times1}$

Simplifying, we get,

30

Thus, the total ways is 30

The number of favorable cases is given by

$30-6=24$

Thus, the number of favorable cases is 24

The probability that the minimum of the two numbers is less than 4 is given by

$\frac{24}{30}=\frac{4}{5}$

Thus, the probability that minimum of the two numbers is less than 4 is $\frac{4}{5}$

Learn more:

(1) Three numbers are chosen at random without replacement from {1, 2, 3, ...... 8}. The probability that their minimum is 3, given that their maximum is 6, is

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(2) A two digit number is to be formed from the digits 0,1,2,3,4,  without repetition of the digits. Find the probability that the number so  formed is a prime number

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