Question

2. You are shooting at a target twice. The probability of hitting the target on the first shot is 0.3. If you hit the target on that first shot, your confidence increases and the probability of hitting the target on the second shot becomes 0.7. However, if you miss the target on the first shot, your confidence decreases, so that the probability of hitting the target on the second shot becomes 0.15.

a) Show the probability tree summarizing these trials of shooting at the target. Make sure that you include all the properties of the probability tree.

b) What is the probability that you miss the target twice?

Answer 1

a)

scenario	Probabilities	Equation
1St hit on target & 2nd also hit on target	0.21	=0.3*0.7
1st hit on target & 2nd missed on target	0.09	=0.3*0.3
1st missed on target & 2nd hit on target	0.105	=0.7*0.15
1st missed on target & 2nd also missed on target	0.595	=0.7*0.85

b) probanility for missing the target twice

1st missed on target & 2nd also missed on target is 0.595 ,