Question

What is the theoretical probability that your five best friends all have telephone numbers ending in 3? (Hint: first determine the probability of a single telephone number ending with a 3. Then calculate the probability of the five independent events occurring together.) Show your answer as a fraction.

Answer 1

Solution:

Given data :

Number of best friends all have telephone numbers ending in 3 = 5

Now we have to find out:

The probability of numbers ending in 3:

To find out the probability first we have to write the all the possible digits from 0 to 9

i.e., { 0,1,2,3,4,5,6,7,8,9 }

total digits in a telephone number = 10

Now, probability of numbers ending in 3 is ,

p(3) = ending number / total digits in telephone number

= 3/10

= 0.3

Now, probability of the five independent events occurring = p( x1, x2, x3, x4, x5 )

p( x1, x2, x3, x4, x5 ) = p(x1 )*p( x2 )*p( x3 )*p( x4 )*p(x 5)

= ( 3/10 )* ( 3/10 )* ( 3/10 )* ( 3/10 )* ( 3/10 )*

=  $(\frac{3}{10})^{5}$

= 243/100000

$\therefore$ The probability of five independent events occurring, numbers ending in 3 = 243/100000