Question

A number is selected from the numbers 1, 2, 3 , and 4. A second number is selected from the numbers 1,5,6, and 12. Find the probability of the following cases:
(a) The sum of two numbers is greater than 7. ans : 9/17
(b) The product of two numbers is less than 12 ans : 7/16
(c) The difference between two numbers is divisible by 3 ans : 5/16
(d) The product of two numbers is a prime number. ans : 3/16

please tell how the answer come in step by step explanation​


if ans is correct I give you more coins​

Answer 1

Number x can be selected in three ways and corresponding to each such way there are three ways of selecting number y. Therefore, two numbers can be selected in 9 ways as listed :

(1,1),(1,4),(1,9),(2,1),(2,4),(2,9),(3,1),(3,4),(3,9)

So, total number of elementary events = 9

The product xy will be less than 9, if x, and y are chosen in one of the following ways :

(1,1),(1,4),(2,1),(2,4),(3,1)

Therefore, favourable number of elementary events = 5

Therefore, required probability =

9

5