Question

A die is rolled. Find the probability of the given event.
(a) The number showing is a 2;
The probability is :

     
(b) The number showing is an even number;
The probability is :

    
(c) The number showing is greater than 5;
The probability is :     

Answer 1

Solution:

Given: A die is rolled.

Thus sample space for rolling a die is:

S = { 1,2,3,4,5,6 }

n = total outcomes in sample space S = 6

Part a) Find:

P( the number showing is a 2) =............?

we have only one outcome a number 2, thus m = 1

P( the number showing is a 2) = m / n

P( the number showing is a 2) = 1 / 6

Part b) Find:

P( The  number showing is an even number) =..........?

outcomes of Even numbers = { 2,4,6}

m = number of outcomes of Even numbers = 3

Thus

P( The  number showing is an even number) = m / n

P( The  number showing is an even number) = 3 / 6

P( The  number showing is an even number) = 1/2

Part c) Find:

P( The number showing is greater than 5 ) = ..........?

We have only one outcome which is greater than 5 = { 6 }

m = Number of outcomes showing number showing is greater than 5 = 1

Thus

P( The number showing is greater than 5 ) = m / n

P( The number showing is greater than 5 ) = 1/6