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Answer :
a. The probability he hits the target 3 times is 0.2013. b. The probability he hits his target at least twice is 0.9984. c. The probability he hits the target at most 4 times is 0.1074. d. The expected number of shots that hit the target is 8.
a. The probability he hits the target 3 times = (10C3) * (0.8)^3 * (0.2)^7 = 0.2013
b. To calculate the probability he hits his target at least twice, we need to calculate the probability of hitting it twice, hitting it thrice, hitting it four times, ..., hitting it ten times.
So, P(hitting at least twice) = P(hitting twice) + P(hitting thrice) + ... + P(hitting ten times).
Therefore,
P(hitting at least twice) = (10C2) * (0.8)^2 * (0.2)^8 + (10C3) * (0.8)^3 * (0.2)^7 + ... + (10C10) * (0.8)^10 * (0.2)^0 = 0.9984
c. The probability he hits the target at most 4 times = P(hitting 0 times) + P(hitting 1 time) + P(hitting 2 times) + P(hitting 3 times) + P(hitting 4 times)
= (10C0) * (0.8)^0 * (0.2)^10 + (10C1) * (0.8)^1 * (0.2)^9 + (10C2) * (0.8)^2 * (0.2)^8 + (10C3) * (0.8)^3 * (0.2)^7 + (10C4) * (0.8)^4 * (0.2)^6
= 0.1074
d. The expected number of shots that hit the target can be calculated as:
Expected number = 10 * 0.8 = 8
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