Answer:
The probability that she wins the game is 0.364
Step-by-step explanation:
Let H = Hit
Let M = Miss
P(Hit with right hand) = 0.7
P(Hit with right hand) = 1-0.3 = 0.3
P(Hit with left hand) = 0.4
P(Miss with left hand) = 1-0.4 = 0.6
First, we need to highlight possible outcomes.
Let SS = Sample Space
SS = {HHH, HHM, HMH, MHH, HMM, MHM, MMH, MMM}
At this point, we follow the assumption that she starts with her right hand (according to the question)
Out of the possible events, only 3 will have the participant win the game:
Which are:
HHH, HHM and MHH.
P (HHH) + P (HHM) + P (MHH)
P(HHH) = P(Hit with right) and P(Hit with left) and P(Hit with right)
P(HHH) = 0.7 * 0.4 * 0.7
P(HHH) = 0.196
P(HHM) = P(Hit with right) + P(Hit with left) + P(Miss with right)
P(HHM) = 0.7 * 0.4 * 0.3
P(HHM) = 0.084
P(MHH) = 0.084 (Same as above)
Probability that she wins = P (HHH) + P (HHM) + P (MHH) = 0.196 + 0.084 + 0.084
Probability that she wins = 0.364
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