Conditional Probability

Q. Two numbers are selected at random from the integers 1 to 9. If the sum is even, find the probability that both numbers are odd?

1. $\frac{5}{8}$
2. $Noneofthese$
3. $\frac{3}{8}$
4. $\frac{13}{204}$

Q. A die is thrown twice and the sum of the numbers appearing is observed to be 9. What is the conditional probability that the number 4 has appeared at least once?

1. $Noneofthese$
2. $\frac{1}{2}$
3. $\frac{2}{3}$
4. $\frac{3}{4}$

Q. Three numbers are to be selected at random without replacement from the set of numbers {1, 2, ... n}. The conditional probability that the third number lies between the first two if the first number is known to be smaller than the second is :

1. $\frac{1}{3}$
2. $\frac{5}{6}$
3. $\frac{2}{3}$
4. $\frac{7}{12}$

Q. A bag contains 6 red and 9 blue balls. Two successive drawing of four balls are made such that the balls are not replaced before the second draw. Find the probability that the first draw gives 4 red balls and second draw gives 4 blue balls.

1. $\frac{7}{715}$
2. None of these
3. $\frac{3}{715}$
4. $\frac{15}{233}$

Q. Urn A contains six red and four black balls and urn B has four red and six black balls. One ball is drawn at random from urn A and placed in urn B. Then one ball is transferred at random from urn B to urn A. If one ball is now drawn at random from urn A, find the probability that is red.

1. $\frac{23}{55}$
2. $\frac{32}{65}$
3. $\frac{32}{55}$
4. $\frac{56}{65}$

Q. A consignment of 15 wristwatches contains 4 defectives. The wristwatches are selected at random, one by one and examined. The ones examined are not put back. What is the probability that ninth one examined is the last defective?

1. $\frac{17}{195}$
2. $\frac{11}{195}$
3. $\frac{8}{195}$
4. $\frac{16}{195}$

Q. Two dices are thrown. The probability that the sum of the numbers coming up on them is 9, if it is known that the number 5 always occurs on the first die, is

1. $\frac{1}{6}$
2. $\frac{1}{3}$
3. $\frac{2}{3}$
4. $\frac{1}{2}$

Q.

If A and B are two events such that P(A) = 0.4, P(B) = 0.8 and $P\left(\frac{B}{A}\right)$ = 0.6, find P(A $\cup$ B)

1. 0.24

2. 0.96

3. 0.04

4. none of these

Q. A and B have less than 6 diamonds each. What is the probability that the sum of the diamonds they have is more than 3 but less than 7?

1. $\frac{3}{5}$
2. $\frac{9}{25}$
3. $\frac{4}{9}$
4. $\frac{2}{3}$

Q. In a one day cricket match played between two teams, in an innings a team can lose a maximum of ten wickets. Find the probability that in a given match the two teams will together lose more than 5 but less than 12 wickets?

1. $0.415$
2. $\frac{51}{121}$
3. $\frac{5}{11}$
4. $0.585$