probability

Question

1)  If a fair coin is tossed 4 times, what is the probability that you will get exactly 3 heads?

 
2)  The chance that the traffic lights are against you on the way to work is 0.6.  If you have to go through 3 sets of lights, what is the probability that they will all show green?

 

Answer 1

1)  Binomial distribution:  uses binomial coefficients  nCr  where n=4, r = 0, 1,...4 multiplied by (½)⁴ = 1/16

 

P(0 heads) = 1•1/16 = 0.0625 

P(1 head) = 4•1/16  

P(2 heads) = 6•1/16  = 0.375 

P(3 heads) = 4•1/16   = 0.25

P(4 heads) = 1•1/16 

 

2) The chance that the traffic lights are against you on the way to work is 0.6. If you have to go through 3 sets of lights, what is the probability that they will all show green?

= 0.4³ = 8/125 = 0.064