Question

10. Three candidates participated in a shooting game. There are required to shoot a target and each of them is given only a chance. Let K; represent the event that candidate number i shot the target, i=1, 2,3. If every shot is independent with probabililties P(K1)=0.5, P(K2)=0.8 and P(K3)=0.9, evaluate the probability that (i) exactly a participant shot the target? (ii) none of them shoot the target? (iii) at least there is a shot at the target?

Answer 1

Ansi- 10 Guven that the probabilities of shooting a target for there candidates are as belowin P( k ) = 0.5 0 P(K2) < 0.8 - © PC kg) -0.9. 3 Also given that the shots are independent. ② from ears , 6 & ③ consider Probability that exactly a participant shot the target = P(A) = ?

P(A)= Probability Probability that that first candidate shot the target and remaining two candidates miss the shot Probability that second candidate shot the target and remaining two candidates muss (OR) the shot (OR) р Probability that third candidate shot the target and remaining two candidates miss the shot. - P(A) = P(K) P(ks) & (ks)' + P(K)' P(ks) P(ks) + - P(K) PC Ke)' PC ks) = P(K) {1- PCk]] [1- P(ks)] + [l-PC k)] PC ks) {1- PCko] + [1- P(K)] [1- P(kz)] p(ks)

P(A) = (0.5) (1-0.8) (1-0.9) & (1.0.5) (0.8) (1-0.9) & (1-05) (1-0.8) (0.9) P(A) = (0.5) (0.2) (ool) + (0.5) (0.8) Coold+ (0.5) (0.2) (0.9) z o.14 @ from Egy ,@ {®, consider, Probability that none of the three candidates Shoot the target = P(B) = ? (B) = P(kx) P (ke) PC ks) = {1- PCk]] [ 1 - P(K)] [1 - P(ks)] (-0.5)(1-0-8) C1-0.9) - (0.5) (0.2) CO.D = 0.01 (p(B) = 0.01

conside targeability that (i) from part Cir), consider Probability that atleast there is a shot at the target - ple) = ? & P(c) = 1- probability that none of them shot = |- PCB) = 1-0,01 = 0.99 the target un [PCC) = 0.99