Question

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 4 consecutive times and the ball lands on a black slot each time. What is the probability that the ball will land on a block slot on the next spin? (b) You watch a roulette wheel spin 300 consecutive times and the ball lands on a black slot each time. What is the probability that the ball will land on a black slot on the next spin? (c) Are you equally condent of your answers to parts (a) and (b)? Why or why not?

Answer 1

Given:

Number of red slots = 18

Number of black slots = 18

Number of green slots = 2

Total number of slots = 18+18+2 = 38

Probability = number of favourable outcomes/total number of outcomes

a) You watch a roulette wheel spin 4 consecutive times and the ball lands on a black slot each time.

The probability that the ball will land on a black slot on the next spin :

P(ball will land on a black slots | previous 4 spins are black)

= P(black) ....... (because each spin is independent so whatever slot on which ball land in previous spin it will not affect.

= 18/38

= 0.4737

Therefore the probability that ball will land on a black slot on the next spin is 0.4737.

b) You watch a roulette wheel spin 300 consecutive times and the ball lands on a black slot each time.

The probability that the ball will land on a black slot on the next spin :

P(ball will land on black slots | previous 300 spins are balck)

= P(black)........(each event are independent)

= 18/38

= 0.4737

Therefore the probability that the ball will land on a black slot on the next spin is 0.4737.

c) No, 300 spins all come up black may provide more evidence that the roullet wheel is rigged and the probability of a ball landing on black my be actually greater than 0.4737