class 12

Math

Algebra

Probability I

Consider 5 independent Bernoulli.s trials each with probability of success p. If the probability of at least one failure is greater than or equal to $3231 $, then p lies in the interval :

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Three married couples sit in a row. Find the probability that no husband sits with his wife.

Probability if n heads in 2n tosses of a fair coin can be given by

A natural number is chosen at random from the first 100 natural numbers. The probability that x + $x100 >50$ is

Eight players $P_{1},P_{2},…,P_{8}$ play a knock-out tournament. It is known that whenever the players $P_{i}$ and $P_{j}$ play, the player $P_{i}$ will win if $i<j$. Assuming that the players are paired at random in each round, what is the probability that the player $P_{4}$ reaches the final?

Let $ω$ be a complex cube root of unity with $ω=1$. A fair die is thrown three times. If $r_{1},r_{2}$ and $r_{3}$ are the numbers obtained on the die, then the probability that $ω_{r_{1}}+ω_{r_{2}}+ω_{r_{3}}=0$ is

The sum of two positive quantities is equal to 2n. Find the probability that their product is not less than $3/4$ times their greatest product.

Three students A and B and C are in a swimming race. A and B have the same probabilityof winning and each is twice as likely to win as C. Find the probability that B or C wins. Assume no two reach the winning point simultaneously.

A four figure number is formed of the figure 1, 2, 3, 5 with no repetition. The probability that the number is divisible by 5 is