Is an experiment, positive and negative values are equally likely to occur. The probability of obtaining at most one negative value in five trials is

There are two containers with one containing $$4$$ red and $$3$$ green balls and the other containing $$3$$ blue balls and $$4$$ green balls. One ball is drawn at random from each container. The probability that one of the balls is red and the other is blue will be ___________.

The standard normal probability function can be approximated as $$$F\left( {{X_N}} \right) = {1 \over {1 + \exp \left( { - 1.7255{X_N}{{\left| {{X_N}} \right|}^{0.12}}} \right)}}\,\,\,$$$
$$\,{X_N} = $$ standard normal deviate. If mean and standard deviation of annual precipitation are $$102$$ cm and $$27$$ cm respectively, the probability that the annual precipitation will be $$b/w$$ $$90$$ cm and $$102$$ cm is

A hydraulic structure has four gates which operate independently. The probability of failure of each gate is $$0.2.$$ Given that gate $$1$$ has failed, the probability that both gates $$2$$ and $$3$$ will fail is