Conditional Probability

A letter is known to have come from either TATANAGAR or CALCUTTA. On the envelope, just two consecutive letters, TA, are visible. The probability that the letter has come from CALCUTTA is

A bag contains $6$ red and $4$ green balls. A fair die is rolled and a number of balls equal to that appearing on the die is chosen from the bag at random. The probability that all the balls selected are red is

A pair of unbiased dice is rolled together till a sum of either $5$ or $7$ is obtained. The probability that $5$ comes before $7$ is

If two events $A$ and $B$ such that $P(A')=0.3,\ P(B)=0.5$ and $P(A\cap B)=0.3$, then $P(B\mid A\cup B')$ is

An anti-aircraft gun fires a maximum of four shots. Probabilities of hitting in the 1st, 2nd, 3rd, and 4th shot are 0.4, 0.3, 0.2 and 0.1 respectively. Find the probability that the gun hits the plane.

A man has 5 coins: 2 double-headed 1 double-tailed 2 normal He randomly picks a coin and tosses it. Probability that the lower face is a head is:

The probability that a man who is 85 yrs old will die before attaining the age of 90 is $1/3$. $A_1, A_2, A_3, A_4$ are four persons aged 85 yrs. The probability that $A_1$ will die before attaining 90 and will be the first to die is:

A and B are independent witnesses. Probability A speaks the truth = $x$, Probability B speaks the truth = $y$. If both agree on a statement, the probability that the statement is true is:

A random variable $X$ has the probability distribution: \[\begin{array}{c|ccccccccc} x & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\ \hline P(X=x) & a & 3a & 5a & 7a & 9a & 11a & 13a & 15a & 17a \end{array} \]The value of $a$ is:

An anti-aircraft gun fires at a plane. Probabilities of hitting at slots 1,2,3,4 are $0.4,;0.3,;0.2,;0.1$. Probability that the gun hits the plane is

If A and B are two events such that $P(A \cup B)=\frac{5}{6}$ , $P(A \cap B)=\frac{1}{3}$ and $P(\overline{B})=\frac{1}{2}$, then the events A and B are

A student takes a quiz consisting of 5 multiple choice questions. Each question has 4 possible answers. If a student is guessing the answer at random and answer to different are independent, then the probability of atleast one correct answer is

A box contains 3 coins, one coin is fair, one coin is two headed and one coin is weighted, so that the probability of heads appearing is $\frac{1}{3}$ . A coin is selected at random and tossed, then the probability that head appears is

A chain of video stores sells three different brands of DVD players. Of its DVD player sales, 50% are brand 1, 30% are brand 2 and 20% are brand 3. Each manufacturer offers one year warranty on parts and labor. It is known that 25% of brand 1 DVD players require warranty repair work whereas the corresponding percentage for brands 2 and 3 are 20% and 10% respectively. The probability that a randomly selected purchaser has a DVD player that will need repair while under warranty, is:

A is targeting B, B and C are targeting A. Probability of hitting the target by A, B and C are $\frac{2}{3}, \frac{1}{2}$ and $\frac{1}{3}$ respectively. If A is hit then the probability that B hits the target and C does not, is

A computer producing factory has only two plants T₁ and T₂ produces 20% and plant T₂ produces 80% of the total computers produced. 7% of the computers produced in the factory turn out to be defective. It is known that P (computer turns out to be defective given that it is produced in plant T₁ 10P(computer turns out to be defective given that it is produced in plant T₂ ). A computer produced in the factory is randomly selected and it does not turn out to be defective. Then the probability that it is produced in plant T₂ is