Probability

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# Probability

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Tickets for movies in a particular theatre have numbers from 1 to 100 printed on them with each ticket having a unique number. The tickets are sold in a random order. Three people go to the theatre and buy tickets, when all the tickets are available. What is the probability that exactly one person's seat is in the range of 6 to 50?

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each of 2 persons tosses three fair coins. The probability that they obtain the same no of heads is?

number of possible outcomes when  3 fair coins are tossed => 2^3

{ TTT , TTH , THH , HHH , HHT , HTT , HTH , THT}

Probability of A getting 3 heads => 1/8
So probability that both will get  3 heads is 1/8 x 1/8 = 1/64

Probability of A getting 2 heads => 3/8
so probabilty that bothwill get  2 heads => 3/8 x 3/8

Similarly probability of getting 1 heads => 3/8 x 3/8
and probabilty of getting o heads => 1/8 x 1/8

2/64 + 18/64 = 5/16

but the ans is 5/16

1/64 + 1/64 + 9/64 +9/64 = 5/16.

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2 persons a and b throw a coin alternatively till one of them gets head and wins the game . what are their respectively probability of winning?

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fanne-khan Mathematician was asked to solve for the roots of the function,

F(x) = x4 – x3 + 2x2 -4x – 8

If the mathematician gave only one answer, what is the probability that his answer was the lowest possible real root given that his answer was correct and a real root of the function indeed?

0.5

0.33

0.25

None of these

x⁴ - x³ + 2x² -4x -8 = 0

( x +1) ( x -2) ( x² +4) = 0

x = -1 , 2 ± 2i

Two real , two imaginary roots.

Probability of getting smallest real root : 1/2:

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A coin of radius 3 cm is randomly dropped on a square floor full of square shaped tiles of side 10 cm each. What is the probability that the coin will land completely within a tile?

If the centre of the coin falls anywhere on smaller square , the coin lies entirely within the bigger square (tile). The probability that the coin lies entirely within a tile is : (area of smaller square)/( area of the bigger sqaure ) = 16/100 = 0.16

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A teacher selects 23 speakers to speak in the class. What is the probability that A is followed by B and B is followed by C?

Sir, does this mean that they are speaking consecutively or we will consider it to be not necessarily consecutive(and this probability is 1/6)?

can be any number of persons in between including zero.

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Two points A and B are picked on a circle with a unit radius. What is the probability that the chord AB has at least length 1 unit?

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