Probability

Out of 7 constants and 4 vowels, words are formed each having 3 constants 2 vowels. The number of such words that can be formed is

• 210

• 25200

• 2520

• 302400

Let A and B be two events such that $\mathrm{P}\left(\mathrm{A} \cap \mathrm{B}\right) = \frac{1}{6}, \mathrm{P}(\mathrm{A} \cup \mathrm{B}) = \frac{31}{45} \mathrm{and} \mathrm{P}\left(\overline{\mathrm{B}}\right) = \frac{7}{10}$ then

• A and B are independent

• A and B are mutually exclusive

• $\mathrm{P}\left(\frac{\mathrm{A}}{\mathrm{B}}\right) < \frac{1}{6}$

• $\mathrm{P}\left(\frac{\mathrm{B}}{\mathrm{A}}\right) < \frac{1}{6}$

If ${}^{\mathrm{n}}\mathrm{C}_{\mathrm{r} - 1} = 36, {}^{\mathrm{n}}\mathrm{C}_{\mathrm{r}} = 84 \mathrm{and} {}^{\mathrm{n}}\mathrm{C}_{\mathrm{r} + 1} = 126, \mathrm{then} \mathrm{the} \mathrm{value} \mathrm{of} {}^{\mathrm{n}}\mathrm{C}_8 \mathrm{is}$

• 10

• 7

• 9

• 8

In a group of 14 males and 6 females. 8 and 3 of the males and females, respectively are aged above 40 yr. The probability that a person selected at random from the group is aged above 40 yr given that the selected person is a female, is

• $\frac{2}{7}$

• $\frac{1}{2}$

• $\frac{1}{4}$

• $\frac{5}{6}$

In a certain town, 60% of the families own a car, 30% own a house and 20% own both car and house. If a family is randomly chosen, then what is the probability that this family owns a car or a house but not both?

• 0.5

• 0.7

• 0.1

• 0.9

If the letters of the word 'PROBABILITY' are written down at random in a row, then probability that two B's are together, is

• $\frac{2}{11}$

• $\frac{10}{11}$

• $\frac{3}{11}$

• $\frac{6}{11}$

A person goes to office by car, scooter, bus and train, probability of which are 1/7, 3/7, 2/7 and 1/7, respectively. Probability that he reaches office late, if he takes car, scooter, bus or train is 2/9, 1/9, 4/9, and 1/9, respectively. Given that he reached office in time, the probability that he travelled by a car, is

• 1/7

• 2/7

• 3/7

• 4/7

Ram is visiting a friend. Ram knows that his friend has 2 children and 1 of them is a boy. Assuming that a child is equally likely to be a boy or a girl, then the probability that the other child is a girl, is

• 1/2

• 1/3

• 2/3

• 7/10

Out of 7 consonants and 4 vowels, the number of words (not necessarily meaningful) that can be made, each consisting of 3 consonants and 2 vowels is,

• 24800

• 25100

• 25200

• 25400

A fair six-faced die is rolled 12 times. The probability that each face turns up twice is equal to

• $\frac{12!}{6! 6! 6^{12}}$

• $\frac{2^{12}}{2^6{6}^{12}}$

• $\frac{12!}{2^6{6}^{12}}$

• $\frac{12!}{6^2{6}^{12}}$