Question:
Alfie tossed a paper cup in the air 150 times and recorded the side it landed on.
Right side up = 60 Upside down = 53 Side = 37
If Alfie tosses the paper cup 100 more times what is the expected number of times the cup will land on its side?
Answer:
The expected number of times the cup will land on its side is 25 times
Step-by-step explanation:
Given
[tex]Right = 60[/tex]
[tex]Upside\ down = 53[/tex]
[tex]Side = 37[/tex]
Required
First, we calculate the probability of landing on side
[tex]P(Side) = \frac{n(Side)}{Total}[/tex]
[tex]P(Side) = \frac{37}{150}[/tex]
[tex]P(Side) = 0.247[/tex]
Next, we calculate the expected value; E(x) using:
[tex]E(x) = n * P(x)[/tex]
When tossed 100 more times:
n = 100 and P(x) = P(Side) = 0.247
So:
[tex]E(x) = 100 * 0.247[/tex]
[tex]E(x) = 24.7[/tex]
[tex]E(x) = 25[/tex] --- approximated
Hence, it is expected that it will land on its side 25 times
