Question

if a pair of standard dice are rolled what is the probability that one die shows a six but not both of them. reduced fraction answer​

Answer 1

Answer:

$P=\frac{5}{18}$

Step-by-step explanation:

we know that

The probability of an event is the ratio of the size of the event space to the size of the sample space.  

The size of the sample space is the total number of possible outcomes  

The event space is the number of outcomes in the event you are interested in.  

so  

Let

x------> size of the event space

y-----> size of the sample space  

if a die is rolled the sample space is

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

if two dice rolled the sample space is

$\{1,2,3,4,5,6\}*\{1,2,3,4,5,6\}$

so

The possible pairs are

$y=6*6=36$

The size of the event space x is

$\{(1,6),(2,6),(3,6),(4,6),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5)\}$

$x=10$

$P=\frac{x}{y}$

substitute

$P=\frac{10}{36}$

Simplify

$P=\frac{5}{18}$