An amateur archer has 4 arrows and shoots at a balloon placed in the center of a target. The probability of hitting the target on the first shot is 30\%. In successive launches the aim improves, so on the second it is 40\%, on the third 50\% and on the fourth 60\%. It is requested:\ a) (1 point) Calculate the probability that the balloon has burst without needing to make the fourth shot.\ b) (0.5 points) Calculate the probability that the balloon remains intact after the fourth shot.\ c) (1 point) In an exhibition ten professional archers participate, who hit 85\% of their shots. Calculate the probability that among the 10 exactly 6 balloons have burst on the first shot.
An amateur archer has 4 arrows and shoots at a balloon placed in the center of a target. The probability of hitting the target on the first shot is 30\%. In successive launches the aim improves, so on the second it is 40\%, on the third 50\% and on the fourth 60\%. It is requested:\
a) (1 point) Calculate the probability that the balloon has burst without needing to make the fourth shot.\
b) (0.5 points) Calculate the probability that the balloon remains intact after the fourth shot.\
c) (1 point) In an exhibition ten professional archers participate, who hit 85\% of their shots. Calculate the probability that among the 10 exactly 6 balloons have burst on the first shot.