Question

In a lottery​ game, the jackpot is won by selecting five different whole numbers from 1 through 37 and getting the same five numbers​ (in any​ order) that are later drawn. In the Pick 5 ​game, you win a straight bet by selecting five digits​ (with repetition​ allowed), each one from 0 to​ 9, and getting the same five digits in the exact order they are later drawn. The Pick 5 game returns ​$50,000 for a winning​ $1 ticket. Complete parts​ (a) through​ (c) below:a. What is the probability of winning a jackpot in this​ game? ​P(winning a jackpot in this ​game)= ________b. In the Pick 5 ​game, you win a straight bet by selecting five digits​ (with repetition​ allowed), each one from 0 to​ 9, and getting the same five digits in the exact order they are later drawn. What is the probability of winning this​ game? ​P(winning the Pick 55​game)= ______________c. The Pick 5 game returns ​$50,000 for a winning​ $1 ticket. What should be the return if the lottery organization were to run this game for no​ profit? ​

Answer 1

Answer:

The probability of winning a jackpot is $P = 0.000003$

The probability of winning the pick 5 game  is  $P_a = 0.00001$

The earning of the lottery organisation if the game were to be runed for no profit is  $x =$$10 000

Step-by-step explanation:

From the question

    The sample size is  n= 37

    The number of selection is  $r = 5$

Now the number of way by which these five selection can be made is mathematically represented as

         $\left n} \atop {}} \right.C_r = \frac{n!}{(n-r)!r! }$

Now  substituting values

         $\left n} \atop {}} \right.C_r = \frac{37!}{(37-5)!5! }$

          $\left n} \atop {}} \right.C_r = 333333.3$

Now the probability of winning  a jackpot from any of the way of selecting 5 whole number from 37 is mathematically evaluated as

         $P = \frac{1}{333333.3}$

        $P = 0.000003$

Now the number of ways of selecting 5 whole number from 0 to 9 with repetition is mathematically evaluated as

        $k = 10^5$

Now the probability of winning the game is

      $P_a = \frac{1}{10^5}$

      $P_a = 0.00001$

We are told that for a $1 ticket that the pick 5 game returns $50 , 000

  Generally the expected value is mathematically represented as

           $E(X) = x * P(X =x )$

In this question the expected value is  $1

So

          $1 = x * 0.00001$

So      $x = \frac{1}{0.00001}$

        $x =$$10 000