R S Aggarwal Solutions for Exercise 2: EXERCISE

A town has two fire-extinguishing engines, functioning independently. The probability of availability of each engine when needed is $0.95$. What is the probability that an engine is available when needed?

(Write answer in decimal form)

A machine operates only when all of its three components function. The probabilities of the failures of the first, second and third components are $0.14, 0.10$ and $0.05$, respectively. What is the probability that the machine will fail?

(Write answer in decimal form).

An anti-aircraft gun can take a maximum of $4$ shots at an enemy plane moving away from it. The probabilities of hitting the plane at the first, second, third and fourth shots are $0.4, 0.3, 0.2$ and $0.1$ respectively. What is the probability that at least one shot hits the plane?

(Write answer in decimal form)

Let ${\mathrm{S}}_1$ and ${\mathrm{S}}_2$ be the two switches and let their probabilities of working be given by $\mathrm{P}\left({\mathrm{S}}_1\right)=\frac{4}{5}$ and $\mathrm{P}\left({\mathrm{S}}_2\right)=\frac{9}{10}$. If the probability that the current flows from the terminal $\mathrm{A}$ to terminal $\mathrm{B}$ when ${\mathrm{S}}_1$ and ${\mathrm{S}}_2$ are installed in series as shown below is $\mathrm{p}$, then the value of $25\mathrm{p}$ is

Let $S_1$ and $S_2$ be two the switches and let their probabilities of working be given by $P\left(S_1\right)=\frac{2}{3}$ and $P\left(S_2\right)=\frac{3}{4}$ Find the probability that the current flows from terminal $A$ to terminal $B$, when $S_1$ and $S_2$ are installed in parallel, as shown below:  

(Write answer in fraction form)

A coin is tossed. If a head comes up, a die is thrown, but if a tail comes up, the coin is tossed again. Find the probability of obtaining two tails.

(Write answer in fraction form).

A coin is tossed. If a head comes up, a die is thrown, but if a tail comes up, the coin is tossed again. Find the probability of obtaining a head and the number $6$.

(Write answer in fraction form)

A coin is tossed. If a head comes up, a die is thrown, but if a tail comes up, the coin is tossed again. Find the probability of obtaining a head and an even number. (Write the answer in simplest fraction form)