Respuesta :
Answer:
We estimate to have 8.33 times the number 6 in 50 trials.
Step-by-step explanation:
Let us consider a success to get a 6. In this case, note that the probability of having a 6 in one spin is 1/6. We can consider the number of 6's in 50 spins to be a binomial random variable. Then, let X to be the number of trials we get a 6 out of 50 trials. Then, we have the following model.
[tex]P(X=k) = \binom{50}{k}(\frac{1}{6})^k(\frac{5}{6})^{50-k}[/tex]
We will estimate the number of times that she spins a 6 as the expected value of this random variable.
Recall that if we have X as a binomial random variable of n trials with a probability of success of p, then it's expected value is np.
Then , in this case, with n=50 and p=1/6 we expect to have [tex]\frac{50}{6}[/tex] number of times of having a 6, which is 8.33.
Answer:
Hence, Stacy will spin 6, Â 8.33 times out of her n = 50 attempts.
Step-by-step explanation:
Solution:-
- First thing we need to note that the probability of getting any number 1 , 2 , 3 , 4 , 5 or 6 is independent from each successive n trials.
- We will assume spinner to be unbiased, i.e the section of each number has the same dimensions (area). Then the probability to get any number of the spinner is = 1 / 6.
- We will define a random variable X : The number of times Stacy gets a 6 on n = 50 trials of spin.
- The random variable X has the probability of success p = the probability to get a 6 on each trial is 1/6. The probability remains same for each trial, so we can assume that RV X follows binomial distribution:
          X ~ Bin ( n , p )
          X ~ Bin ( 50 , 1/6 )
- The pmf of the Binomial distribution is given by:
         P ( X = r ) = n C r * ( p )^r * ( 1 - p )^( n - r )
Where, r = The number times she gets a 6 on her spins.
- The expected number of times she Stacy gets a 6 for n = 50 trials is given:
          E ( X ) = n*p
               = 50 * 1/6
               = 8.33 times Â
Hence, Stacy will spin 6, Â 8.33 times out of her n = 50 attempts.
