Question

roll 2 dice. predict in 60 rolls how many times both dice will land on an even number. next, simplify the fraction. $\frac{9}{36}=\frac{?}{}$ enter the numerator.

Explanation:

Step1: Find probability of both dice landing on even

The probability that a single - die shows an even number is $\frac{3}{6}=\frac{1}{2}$ (since there are 3 even numbers out of 6 possible outcomes). Since the rolls of the two dice are independent events, the probability that both dice land on an even number is $\frac{1}{2}\times\frac{1}{2}=\frac{1}{4}$.

Step2: Predict number of times in 60 rolls

If the probability of an event is $p$ and the number of trials is $n$, the expected number of times the event occurs is $E = n\times p$. Here, $n = 60$ and $p=\frac{1}{4}$, so $E=60\times\frac{1}{4}=15$.

Step3: Simplify the fraction $\frac{9}{36}$

Find the greatest - common divisor (GCD) of 9 and 36. The factors of 9 are 1, 3, and 9. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36. The GCD of 9 and 36 is 9. Divide both the numerator and the denominator by 9: $\frac{9\div9}{36\div9}=\frac{1}{4}$. The numerator of the simplified fraction is 1.

Answer:

1