A one-way, single lane road has traffic that consists of $30 \%$ trucks and $70 \%$ cars. The speed of trucks (in km/h) is a uniform random variable on the interval ( 30,60 ), and the speed of cars (in km/h) is a uniform random variable on the interval $(40,80)$. The speed limit on the road is $50 \mathrm{~km} / \mathrm{h}$. The percentage of vehicles that exceed the speed limit is ________ (rounded off to 1 decimal place).

Note: $X$ is a uniform random variable on the interval ( $\alpha, \beta$ ), if its probability density function is given by

$$ f(x)= \begin{cases}\frac{1}{\beta-\alpha} & \alpha < x < \beta \\ 0 & \text { otherwise }\end{cases} $$

In a sample of 100 heart patients, each patient has 80% chance of having a heart attack without medicine X. It is clinically known that medicine X reduces the probability of having a heart attack by 50%. Medicine X is taken by 50 of these 100 patients. The probability that a randomly selected patient, out of the 100 patients, takes medicine X and has a heart attack is

The return period of a large earthquake for a given region is 200 years. Assuming that earthquake occurrence follows Poisson’s distribution, the probability that it will be exceeded at least once in 50 years is ______________ % (rounded off to the nearest integer).

A pair of six-faced dice is rolled twice. The probability that the sum of the outcomes in each roll equals 4 in exactly two of the three attempts is _________ (round off to three decimal places).