Question

The state lottery board is examining the machine that randomly picks the lottery numbers. On each trial, the machine outputs a ball with one of the digits 0 through 9 on it. (The ball is then replaced in the machine.) Answer the following. Round your answers to the nearest thousandths

Answer 1

Case: Probability

As more trials are conducted, the experimental probability generally gets closer to the theoretical probability.

Method:

a) Experimental probability of getting an odd number

The possibilities are: 1, 3, 5, 7, and 9.

`\begin{gathered} Pr(odd) \\ =(n(odd))/(n(total)) \\ =(3+0+4+1+3)/(20) \\ =(11)/(20) \end{gathered}`

b) If the machine was fair, the theoretical probability for 2 trials is:

`Pr(odd)=(1)/(2)`

c) With a small number of trials, it is surprising when the experimental probability is much greater than the theoretical probability

Final answers: (Nearest thousandths)

a) 0.550

b) 0.500

c) With a small number of trials, it is surprising when the experimental probability is much greater than the theoretical probability