leo is going to use a random number generator 400 times. each time he uses it, he will get a 1, 2, 3, 4, or…

leo is going to use a random number generator 400 times. each time he uses it, he will get a 1, 2, 3, 4, or 5. what is the best prediction for the number of times that leo will get an odd number? choose 1 answer: a exactly 133 times b close to 133 times but probably not exactly 133 times c exactly 240 times d close to 240 times but probably not exactly 240 times
Answer
Explanation:
Step1: Determine probability of odd number
The odd - numbered outcomes among 1, 2, 3, 4, 5 are 1, 3, 5. So there are 3 odd - numbered outcomes out of 5 total outcomes. The probability of getting an odd number in a single trial, $P(\text{odd})=\frac{3}{5}$.
Step2: Calculate expected number of odd numbers
Leo uses the random number generator $n = 400$ times. The expected number of times to get an odd number is $E=n\times P(\text{odd})$. Substitute $n = 400$ and $P(\text{odd})=\frac{3}{5}$ into the formula: $E = 400\times\frac{3}{5}=240$. But this is an expected value. In a real - world situation of 400 trials, we will probably not get exactly 240 odd numbers.
Answer:
D. Close to 240 times but probably not exactly 240 times