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

• $\frac{2}{11}$

• $\frac{10}{11}$

• $\frac{3}{11}$

• $\frac{6}{11}$

632.

A fair coin is tossed-at a fixed number of times. If the probability of getting exactly 3 heads equals the probability of getting exactly 5 heads, then the probability of getting exactly one head is

• 1/64

• 1/32

• 1/16

• 1/8

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

• $\frac{12!}{6! 6! 6^{12}}$

• $\frac{2^{12}}{2^6{6}^{12}}$

• $\frac{12!}{2^6{6}^{12}}$

• $\frac{12!}{6^2{6}^{12}}$

A poker hand consists of 5 cards drawn at random from a well-shuffled pack of 52 cards. Then, the probability that a poker hand consists of a pair and a triple of equal face values (for example, 2 sevens and 3 kings or 2 aces and 3 queens, etc.) is

• $\frac{6}{4165}$

• $\frac{23}{4165}$

• $\frac{1797}{4165}$

• $\frac{1}{4165}$

Each of a and b can take values 1 or 2 with equal probability. The probability that the equation ax² + bx + 1= 0 has real roots, is equal to

• $\frac{1}{2}$

• $\frac{1}{4}$

• $\frac{1}{8}$

• $\frac{1}{16}$

Cards are drawn one-by-one without replacement from a well shuffled pack of 52 cards. Then, the probability that a face card (jack, queen or king) will appear for the first time on the third turn is equal to

• $\frac{300}{2197}$

• $\frac{36}{85}$

• $\frac{12}{85}$

• $\frac{4}{51}$

There are two coins, one unbiased with probaility $\frac{1}{2}$ or getting heads and the other one is biased with probability $\frac{3}{4}$ of getting heads. A coin is selected at random and tossed. It shows heads up. Then, the probability that the unbiased coin was selected is

• $\frac{2}{3}$

• $\frac{3}{5}$

• $\frac{1}{2}$

• $\frac{2}{5}$