Answer:
Hence, Stacy will spin 6, 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
Hence, Stacy will spin 6, 8.33 times out of her n = 50 attempts.