We have a spinner with four places: 5, 6, 7 and 8.
We have to calculate the probability of landing an even number and then landing on a number that is less than 7.
Both events are independent so we can write:
[tex]P(E\&<7)=P(E)\cdot P(<7)[/tex]We can then calculate each probability independently.
The probability of getting an even number is the quotient between the number successful outcomes (2 outcomes: getting a 6 and getting an 8) and the number of possible outcomes) (4 outcomes):
[tex]P(E)=\frac{2}{4}=\frac{1}{2}[/tex]The probability of getting a number that is less than 7 is 2/4 as we have 2 outcomes that are less than 7 (5 and 6) out of 4 possible outcomes.
Then, the probability is:
[tex]P(<7)=\frac{2}{4}=\frac{1}{2}[/tex]Then, the probability of both events together is:
[tex]P(E\&<7)=P(E)\cdot P(<7)=\frac{1}{2}\cdot\frac{1}{2}=\frac{1}{4}=0.25[/tex]We can express this probability as a percentage by multiplying it by 100%:
[tex]P(E\&<7)=0.25\cdot100\%=25\%[/tex]Answer: 25%
