Question

Stacy uses a spinner with six equal sections numbered 2, 2, 3, 4, 5, and 6 to play a game. Stacy spins the pointer 120 times and records the results. The pointer lands 30 times on a section numbered 2, 19 times on 3, 25 times on 4, 29 times on 5, and 17 times on 6. A winning spin is a 2.

Complete the table to find the theoretical and experimental probabilities of winning, and compare the two.

Answer 1

• Theoretical probability of winning=33.3%
• Experimental probability of winning=25%
• The theoretical probability of winning is greater

Explanation:

The six equal sections are numbered 2, 2, 3, 4, 5, and 6.

Number of Outcome of 2 on the Spinner=2

Total Number of Sections=6

Since a winning spin is a 2

The theoretical probability of winning
`=(2)/(6)=(1)/(3)`

In percentage
`=(1)/(3)X100=33.3\%`

In the experimental trial:

Total Number of Trials=120

Number of Outcome of 2=30

Therefore, the experimental probability of winning
`=(30)/(120)=(1)/(4)`

In percentage
`=(1)/(4)X100=25\%`

Since 33.3%>25%, the theoretical probability of winning is greater.