A fair coin is tossed-at a fixed number of times. If the probabil

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 Multiple Choice QuestionsMultiple Choice Questions

631.

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

  • 211

  • 1011

  • 311

  • 611


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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


B.

1/32

Let the coin be tossed n times.

Let getting head is consider to be success.

 p = 12, q = 1 - p = 1 - 12 = 12

It is given that,

P(X = 3) = P(X = 5)

 C3n12312n - 3 = C5n12512n - 5 C3n = C5n n = 3 + 5           Cxn = Cyn  x +y = n n = 8

Now P(X = 1) = C18121128 - 1

                        = C18 × 128                        = 132


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633.

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


634.

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


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635.

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


636.

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

  • 12!6! 6! 612

  • 21226612

  • 12!26612

  • 12!62612


637.

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

  • 64165

  • 234165

  • 17974165

  • 14165


638.

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

  • 12

  • 14

  • 18

  • 116


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639.

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

  • 3002197

  • 3685

  • 1285

  • 451


640.

There are two coins, one unbiased with probaility 12 or getting heads and the other one is biased with probability 34 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

  • 23

  • 35

  • 12

  • 25


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