1) (6 points) The game of roulette involves spinning a wheel with 38 slots: 18 r

Question

1) (6 points) The game of roulette involves spinning a wheel with 38 slots: 18 red, 18 black, and 2 green. A ball is spun onto the wheel and will eventually land in a slot, where each slot has an equal chance of capturing the ball (a) You watch a roulette wheel spin 3 consecutive times and the ball lands on a red slot each time. What is the probability that the ball will land on a red slot on the next spin? (b) You watch a roulette wheel spin 300 consecutive times and the ball lands on a red slot each time. What is the probability that the ball will land on a red slot on the next spin? (c) Are you equally confident of your answers to parts (a) and (b)? Why or why not?

Explanation / Answer

1a) these events are independent

So this means that whatever slot on which ball lands in previous spin it will not affect the next spins

Therefore

a) P(lands on red) = 18 / 38 = 9/19 =0.4736

b) P(lands on red) = 18 / 38 = 9/19 =0.4736

c) Yes we are equally confident for our answer

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