Independent Events

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 form urn A and placed in urn B. Then one ball is transfered at random form urn B to urn A. If one ball is now drawn at random from urn A, find the probability that is red. ?

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

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

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

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

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 atleast once ?

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

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

Q. An unbiased die is tossed twice. Find the probability of getting a 1, 2, 3 or 4 on the first toss and a 4, 5 or 6 on the second toss.

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

Q. Ajay and his wife Kajol appear in an interview for two vacancies in the same post. The probability of Ajay's selection is $\frac{1}{7}$ and that of his wife Kajol's selection is $\frac{1}{5}$. What is the probability that only one of them will be selected?

1. $\frac{2}{7}$
2. $\frac{2}{35}$
3. $\frac{5}{7}$
4. $\frac{1}{5}$

Q. Ajay and his wife Kajol appear in an interview for two vacancies in the same post. The probability of Ajay's selection is $\frac{1}{7}$ and that of his wife Kajol's selection is $\frac{1}{5}$. What is the probability that none of them will be selected?

1. $Noneofthese$
2. $\frac{12}{35}$
3. $\frac{6}{35}$
4. $\frac{24}{35}$

Q. Ajay and his wife Kajol appear in an interview for two vacancies in the same post. The probability of Ajay's selection is $\frac{1}{7}$ and that of his wife Kajol's selection is $\frac{1}{5}$. What is the probability that both of them will be selected?

1. $\frac{1}{35}$
2. $\frac{13}{35}$
3. $\frac{12}{35}$
4. $\frac{1}{12}$

Q. The odds against a husband who is 50 years old living till he is 70 are 7:5 and the odds against his wife who is now 40, living till she is 60 are 5 : 3. Find the probability that at least one of them will be alive 20 years hence.

1. $Noneofthese$
2. $\frac{61}{96}$
3. $\frac{31}{96}$
4. $\frac{41}{70}$