Question

Find the probability of winning a lottery with the following rule. Select the winning numbers from​ 1, 2, . . .​ ,34 . ​(In any order. No​ repeats.)

Answer 1

Complete Question

Find the probability of winning a lottery with the following rule. Select the  six  winning numbers from​ 1, 2, . . .​ ,34 . ​(In any order. No​ repeats.)

Answer:

The  probability is  $P(winning ) = 7.435 *10^{-7}$

Step-by-step explanation:

From the question we are told that

     The  total winning numbers   n =  34

      The total number to select is   r =  6

The total outcome of  lottery is mathematically represented as

      $t_{outcome}) = \left n } \atop {}} \right. C_r$

      $t_{outcome}) = \frac{n! }{(n-r )! r!}$

substituting values

      $t_{outcome}) = \frac{ 34 ! }{(34 - 6 )! 6!}$

      $t_{outcome}) = \frac{ 34 ! }{28 ! 6!}$

     $t_{outcome}) =1344904$

The  number of desired outcome is  

           $t_{desired} = 1$

 this is because the desired outcome is choosing the six winning number

   The probability of winning a lottery is mathematically represented as

      $P(winning ) = \frac{t_{desired}}{t_{outcome}}$

substituting values  

     $P(winning ) = \frac{1}{1344904 }$

      $P(winning ) = 7.435 *10^{-7}$