Probability that neither will score

Question

When Laura and Michelle play in the hockey team, the probability that's Laura will score is 1/3 and that Michelle scores is 1/2.

Find the probability that NEITHER will score in the next game. 

Answer 1

P(Laura scores) = 1/3

Therefore, P(Laura does not score) = 2/3

 

P(Michelle scores) = 1/2

Therefore, P(Michelle does not score) = 1/2

 

P(Laura scores AND Michelle scores) = (1/3)(1/2) = 1/6

P(Laura scores AND Michelle does not score) = (1/3)(1/2) = 1/6

P(Laura does not score AND Michelle scores) = (2/3)(1/2) = 1/3

 

Finally, P(Laura does not score AND Michelle does not score) = (2/3)(1/2) = 1/3.

 

Note: Since these are all the possible outcomes, their probabilities should add up to be 1:

1/3 + 1/3 + 1/6 + 1/6 = 2/3 + 1/3 = 1.