Answer:
Difference between the experimental and the theoretical probability is 2/5 .
Step-by-step explanation:
Spinner is spun 10 times, and experimental probability of landing on a 3 is 1/2, i.e. out of 10 times spinner lands 5 times into 3.
Now, theoretical probability of landing on a 3 is 1/10.
∴ Difference between the experimental and the theoretical probability :
⇒ (1/2) - (1/10)
⇒ 2/5
The difference between the experimental and the theoretical probability is 1/6
The given parameters are:
[tex]\mathbf{n = 10}[/tex] --- the number of times the spinner was spun
[tex]\mathbf{P_e(3) = \frac 12}[/tex] ---- the experimental probability of landing on a 3
To calculate the theoretical probability, we make use of
[tex]\mathbf{P_t(a) = \frac 1s}[/tex]
Where s represents the number of partitions of the spinner.
The spinner has 3 partitions
So, we have:
[tex]\mathbf{P_t(3) = \frac 1{3}}[/tex]
The above equation means that, the theoretical probability of landing on a 3 is 1/3
So, the difference between both probabilities is:
[tex]\mathbf{d = |P_e(3) -P_t(3)|}[/tex]
This gives
[tex]\mathbf{d = |\frac 1{3} - \frac 1{2}|}[/tex]
Take LCM
[tex]\mathbf{d = |\frac {2 - 3}{6}|}[/tex]
[tex]\mathbf{d = |-\frac { 1}{6}|}[/tex]
Remove absolute brackets
[tex]\mathbf{d = \frac { 1}{6}}[/tex]
Hence, the difference is 1/6
Read more about experimental and theoretical probabilities at:
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