KCET (DEMO) MATHS PU1 PROBABILITY PAPER

The mean and the variance of a binomial distribution are 4 and 2 respectively. Then the probability of 2 successes is

For a binomial distribution $$\bar{x}=4, \sigma=\sqrt{3}$$. Then $$\mathrm{P}(\mathrm{X}=\mathrm{r})=$$

If X is Poisson variate with $$P(X=0)=P(X=1)$$, then $$P(X=2)=$$

In a Poisson distribution the variance is m . The sum of the terms in odd places in this distribution is

Two natural numbers $$a$$ and $$b$$ are selected at random. The probability that $$a^{2}+b^{2}$$ is divisible by 7 is

If a and $$b$$ are chosen randomly from the set consisting of numbers $$1,2,3,4,5,6$$ with replacement. Then probability that $$\mathrm{Lt}_{x \rightarrow 0}\left(\frac{a^{x}+b^{x}}{2}\right)^{2 / x}=6$$ is

Thirty-two players ranked 1 to 32 are playing in a knockout tournament. Assume that in every match between any two players, the better-ranked player wins, the probability that ranked 1 and ranked 2 players are winner and runner up respectively, is

A coin is tossed 7 times. Then the probability that at least 4 consecutive heads appear is

A fair coin is tossed 5 times then probability that two heads do not occur consecutively (No two heads come together)

A man throws a die until he gets a number bigger than 3 . The probability that he gets 5 in the last throw

A bag contains 4-balls two balls are drawn from the bag and are found to be white then probability that all balls in the bag are white

A randomly selected year is containing 53 Mondays then probability that it is a leap year

When 5-boys and 5-girls sit around a table the probability that no two girls come together

There are m-stations on a railway line. A train has to stop at 3 intermediate stations then probability that no two stopping stations are adjacent

The probability that randomly selected positive integer is relatively prime to 6