mark is rolling a six - sided number cube repeatedly. his goal is to roll an odd number 17 times. how many…
mark is rolling a six - sided number cube repeatedly. his goal is to roll an odd number 17 times. how many times should mark expect to have to roll the number cube for an odd number to be rolled 17 times? enter your answer in the box to correctly complete the statement. mark should expect to roll the number cube approximately times to roll an odd number 17 times.
Answer
Explanation:
Step1: Determine probability of rolling odd
On a six - sided die, odd numbers are 1, 3, 5. So there are 3 odd numbers out of 6. The probability $p$ of rolling an odd number in a single roll is $p=\frac{3}{6}=\frac{1}{2}$.
Step2: Use expected - value formula
The expected - value formula for a binomial situation (where we want a certain number of successes) is $n=\frac{r}{p}$, where $r$ is the number of desired successes and $p$ is the probability of success in a single trial. Here, $r = 17$ (number of times we want to roll an odd number) and $p=\frac{1}{2}$. So $n=\frac{17}{\frac{1}{2}}=17\times2 = 34$.
Answer:
34