Probability Tes...

Box $$I$$ contains $$5$$ red and $$4$$ blue balls, while box $$II$$ contains $$4$$ red and $$2$$ blue balls. A fair die is thrown. If it turns up a multiple of $$3$$, a ball is drawn from the box $$I$$ else a ball is drawn from box $$II$$. Find the probability of the event ball drawn is from the box $$I$$ if it is blue.

A school has five houses A, B, C, D and E. A class has 23 students, 4 from house A, 8. from house B, 5 from  house C, 2 from house 0 and rest from house E. A single student is selected at random ,to be the class monitor. The probability that the selected student is not from A, Band C is?

There are three different Urns, Urn-I, Urn-II and Urn-III containing 1 Blue, 2 Green, 2 Blue, 1 Green, 3 Blue, 3 Green balls respectively. If two Urns are randomly selected and a ball is drawn from each Urn and if the drawn balls are of different colours then the probability that chosen Urn was Urn-I and Urn-II is

Two aeroplanes $$I$$ and $$II$$ bomb a target in succession. The probability of $$I$$ and $$II$$ scoring a hit correctly are $$0.3$$ and $$0.2$$ respectively. The second plane will bomb only if the first misses the target. The probability that the target is hit by the second plane is

If $$E_{1}$$ and $$E_{2}$$ are two events such that $$\displaystyle P\left ( E_{1} \right )=\frac{1}{4}, P\left ( E_{2} \right )=\frac{1}{2}; P\left ( \frac{E_{1}}{E_{2}} \right )=\frac{1}{4},$$ then choose the correct options.

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Which set is shaded in the above diagram?

Probability of solving specific independently by $$A$$ and $$B$$ are $$\displaystyle\frac { 1 }{ 2 } $$ and $$\displaystyle\frac { 1 }{ 3 } $$ respectively. If both try to solve the problem independently, find the probability that
(i) the problem is solved
(ii) exactly one of them solves the problem.

Given that the events $$A$$ and $$B$$ are such that $$P\left( A \right) = \displaystyle\frac { 1 }{ 2 } ,  P\left( A\cup B \right) = \displaystyle\frac { 3 }{ 5 } $$ and $$P\left( B \right) =p$$. Find $$p$$ if they are (i) mutually exclusive (ii) independent.

A coin is tossed and a single $$6$$-sided die is rolled. Find the probability of landing on the tail side of the coin and rolling $$4$$ on the die.