Given : let $\mathrm{H}$ be head, and $\mathrm{T}$ be tails where as $1,2,3,4,5,6$ be the numbers on the dice which are thrown when a head comes up or else coin is tossed again if its tail....
Given : let $\mathrm{H}$ be head, and $\mathrm{T}$ be tails where as $1,2,3,4,5,6$ be the numbers on the dice which are thrown when a head comes up or else coin is tossed again if its tail....
and 
be two the switches and let their probabilities of working be given by 
and 
Find the probability that the current flows from terminal A to terminal 
, when 
and 
are installed in parallel, as shown below:Solution: Given: $\mathrm{S}_{1}$ and $\mathrm{S}_{2}$ are two swiches whose probabilities of working be given by $\mathrm{P}\left(\mathrm{S}_{1}\right)=\frac{2}{3}$ and...
and be the two switches and let their probabilities of working be given by 
and 
. Find the probability that the current flows from the terminal A to terminal B when and are installed in series, shown as follows:Solution: Given: $S_{1}$ and $S_{2}$ are two swiches whose probabilities of working be given by $\mathrm{P}\left(\mathrm{S}_{1}\right)=\frac{4}{5} \text { and }...
and 
respectively. What is the probability that at least one shot hits the plane?Given:Let $A, B, C$ and $D b e$ first second third and fourth shots whose probability of hitting the plane is given i.e, $\mathrm{P}(\mathrm{A})=0.4, \mathrm{P}(\mathrm{B})=0.3,...
and 
, respectively. What is the probability that the machine will fail?Given: let $A, B$ and $C$ be the three components of a machine which works only if all its three compenents function.the probabilities of the failures of $A, B$ and $C$ respectively is given i.e,...
What is the probability thatGiven: Let $A$ and $B$ be two fire extinguishing engines. The probability of availability of each of the two fire extinguishing engines is given i.e., $\mathrm{P}(\mathrm{A})=0.95$ and...
and 
. In the process of manufacture of part X. 8 out of 100 parts may be defective. Similarly, 5 out of 100 parts of may be defective. Calculate the probability that the assembled product will not be defective.Given: $X$ and $Y$ are the two parts of a company that manufactures an article. Here the probability of the parts being defective is given i.e, $\mathrm{P}(\mathrm{X})=\frac{8}{100}$ and...
in these courses are 
and 
respectively. Find the probabilities that Neelam receives exactly 2 A grades.Given : let $A, B$ and $C$ represent the subjects physics,chemistry and mathematics respectively ,the probability of neelam getting $A$ grade in these three subjects is given i.e, $P(A)=0.2,...
in these courses are and respectively. Find the probabilities that Neelam receivesGiven : let $A, B$ and $C$ represent the subjects physics,chemistry and mathematics respectively ,the probability of neelam getting $A$ grade in these three subjects is given i.e, $P(A)=0.2,...
can hit 2 times in 3 shots. Calculate the probability that
and 
all hit the target
and hit and 
does not hit the target.Given : let $A, B$ and $C$ chances of hitting a target is given i.e, $P(A)=\frac{4}{5}, P(B)=\frac{3}{4}$ and $P(C)=\frac{2}{3}$ $\Rightarrow \mathrm{P}(\bar{A})=\frac{1}{5},...
solving a problem are 
and 
, respectively. If all the three try to solve the problem simultaneously, find the probability that exactly one of them will solve it.Given : let $A, B$ and $C$ be three students whose chances of solving a problem is given i.e, $P(A)=\frac{1}{3}, P(B)=\frac{1}{4}$ and $P(C)=\frac{1}{6}$ $\Rightarrow...
and , respectively. Find the probability that the problem is solved.Given : let $A, B$ and $C$ be three students whose chances of solving a problem is given i.e, $P(A)=\frac{1}{4}, P(B)=\frac{1}{5}$ and $P(C)=\frac{1}{6}$ $\Rightarrow...
, and the probability that B can solve the same problem is \%, find the probability that and will solve the problemGiven : Here probability of $A$ and $B$ that can solve the same problem is given, i.e., $P(A)=\frac{2}{3}$ and $P(B)=\frac{3}{5} \Rightarrow P($ $\bar{A})=\frac{1}{3}$ and...
and that of B’s selection is 
Find the probability thatGiven : $A$ and $B$ appear for an interview, then $P(A)=\frac{1}{6}$ and $P(B)=\frac{1}{4} \Rightarrow P(\bar{A})=\frac{5}{6}$ and $P(\bar{B})=\frac{3}{4}$ Also, $A$ and $B$ are independent. A and...
and that of B’s selection is Find the probability thatGiven : $A$ and $B$ appear for an interview, then $P(A)=\frac{1}{6}$ and $P(B)=\frac{1}{4} \Rightarrow P(\bar{A})=\frac{5}{6}$ and $P(\bar{B})=\frac{3}{4}$ Also, $A$ and $B$ are independent. A and...
, and that of Ved’s rejection is 
Find the probability that at least one of them will be selected.Given : let A denote the event 'Arun is selected' and let B denote the event 'ved is selected'. Therefore, $\mathrm{P}(\mathrm{A})=\frac{1}{4}$ and $\mathrm{P}(\bar{B})=\frac{2}{3} \Rightarrow...
, and that of Vimal’s selection is 
Find the probability that only one of them will be selected.event 'vimal is selected'. Therefore, $\mathrm{P}(\mathrm{A})=\frac{1}{3}$ and $\mathrm{P}(\mathrm{B})=\frac{1}{5}$ Also, $A$ and $B$ are independent .A and not $B$ are independent, not $A$ and $B$...
and be the events such that 
and 
or 
.Given: $A$ and $B$ are the events such that $P(A)=\frac{1}{2}$ and $P(B)=\frac{7}{12}$ and $P(\operatorname{not} A$ or $\operatorname{not} B)=\frac{1}{4}$ To Find: i)if A and B are mutually...
and 
are independent events such that 
and 
, find
i) $\mathrm{P}\left(\overline{E_{1}} \cap \overline{E_{2}}\right)=\mathrm{P}\left(\overline{E_{1}}\right) \times \mathrm{P}\left(\overline{E_{2}}\right)$ since, $P\left(E_{1}\right)=0.3$ and...
and are independent events such that and , find
i) $P\left(E_{1} \cap E_{2}\right)$ We know that, when $E_{1}$ and $E_{2}$ are independent, $\begin{array}{l} P\left(E_{1} \cap E_{2}\right)=P\left(E_{1}\right) \times P\left(E_{2}\right) \\ =0.3...
and are the two events such that 
and 
, show that and are independent events.We know that, Hence, $P\left(E_{1} \cap E_{2}\right)=P\left(E_{1}\right)+P\left(E_{2}\right)-P\left(E_{1} \cup E_{2}\right)$ $=\frac{1}{4}+\frac{1}{3}-\frac{1}{2}$ $=\frac{1}{12}$ Equation 1 Since...
and be the events such that 
and 
. Find:
, when and are mutually exclusive., when 
and 
are independent(i) We know that, When two events are mutually exclusive $P\left(E_{1} \cap E_{2}\right)=0$ Hence, $P\left(E_{1} \cup E_{2}\right)=P\left(E_{1}\right)+P\left(E_{2}\right)$ $\begin{array}{l}...
Let, success in the first draw be getting 3 white balls. Now, the Probability of success in the first trial is $P_{1}(\text { success })=\frac{5_{c_{3}}}{13_{c_{3}}}=\frac{10}{286}=\frac{5}{143}$...
white and 15 black balls. Two balls are drawn in succession without replacement. What is the probability that the first ball is white and the second is black?Let, success in the first draw be getting a white ball. Now, the Probability of success in the first trial is $\mathrm{P}_{1}(\text { success })=\frac{10}{25}$ Let success in the second draw be...
Let, success :bulb chosen is defective .i.e $\frac{5}{30}$ Now, the Probability of success in the first trial is $P_{1}(\text { success })=\frac{5}{30}$ Probability of success in the second trial...
Let, success for the first trail be getting a club. Now, the Probability of success in the first trial is $\mathrm{P}_{1} \text { (success) }=\frac{13}{52}$ let, success for the second trail be...
Let, success : marble drawn is black.i.e Number of black marbles/Total number of marbles $=\frac{3}{7}$ Now, the Probability of success in the first trial is $P_{1}(\text { success })=\frac{3}{7}$...
Let, success : ticket drawn is even.i.e $\frac{8}{17}$ Now, the Probability of success in the first trial is $P_{1}(\text { success })=\frac{8}{17}$ Probability of success in the second trial...