gia performs an experiment where she rolls 2 fair dice. if she performs this experiment 300 times, what is…
gia performs an experiment where she rolls 2 fair dice. if she performs this experiment 300 times, what is the best prediction for the number of repetitions of the experiment that will result in both the dice landing on an odd number?\n100\n50\n60\n75
Answer
Explanation:
Step1: Calculate probability of one - roll event
The probability that a single fair die shows an odd number is $\frac{3}{6}=\frac{1}{2}$ since there are 3 odd numbers (1, 3, 5) out of 6 possible outcomes. Since the rolls of the two dice are independent events, the probability that both dice show odd numbers is $P=\frac{1}{2}\times\frac{1}{2}=\frac{1}{4}$.
Step2: Calculate expected number of occurrences
The expected number of times an event occurs in $n$ trials is given by $E = n\times P$. Here, $n = 300$ and $P=\frac{1}{4}$. So $E=300\times\frac{1}{4}=75$.
Answer:
75