Wheel of fortune is a popular game show on televis ion. contestants spin a wheel and try to guess a correct letter from a word puzzle. if they guess correctly, they earn the dollar amount from the wheel. if they spin “bankrupt” or “lose a turn” they get nothing and can’t play. to the right is an example of the wheel. the outcome of a spin on the wheel is a discrete random variable. consider x the dollar amount spun on the wheel, where bankrupt and lose a turn = $0, and free play = $500. there are 24 wedges on the wheel.
the following table provides the probability mass function for x. round values to 3 decimal places.
x $0 $300 $350 $400 $450 $500 $550 $600 $700 $800 $900 $5,000
count 2 5 1 2 1 3 1 3 1 2 2 1
p(x) 0.083 0.208 0.042 0.083 0.042 0.125 0.042 0.125 0.042 0.083 0.083 0.042
what is the most likely dollar amount?
how likely is it to spin lose a turn or bankrupt?
what is the average dollar amount? show work!
suppose a contestant spins the wheel three times, how likely is it they spin $0 at least one time? show work!