Bernoulli Trials and Binomial Distribution

A die is thrown $7$ times. The chance that an odd number turns up at least $4$ times is

Two players $A$ and $B$ toss $4$ coins and $3$ coins respectively. The probability that both of them get the same number of heads is

Find the minimum number of tosses of a pair of dice, so that the probability of getting the sum of the numbers on the dice equal to $7$ on atleast one toss, is greater than $0.95$. (Given ${\log }_{10} 2=0.3010, {\log }_{10} 3=0.4771$)

A coin is tossed $7$ times. Each time a man calls head. The probability that he wins the toss on more occasions is

Two dice are thrown together $4$ times. The probability that both dice will show same numbers twice is

The probability that a man can hit a target is $\frac{3}{4}$. He tries $5$ times. The probability that he will hit the target at least three times is

India and Pakistan play a $5$ match test series of hockey and the probability of India's winning is $\frac{1}{2}$, then the probability that India wins at least three matches is 

A box contains $20$ identical balls of which $10$ are blue and $10$ are green. The balls are drawn at random from the box one at a time with replacement. The probability that a blue ball is drawn $4^{\mathrm{th}}$ time on the $7^{\mathrm{th}}$ draw is

If a certain missile will hit the target one out of four times and four such missiles are fired at the same time, then what is the probability that the target will be hit atleast once?

If the mean and variance of a binomial distribution are $4$ and $2$, respectively. Then, the probability of at least $7$ successes is

The probability of at least one double six being thrown in $n$ throws with two ordinary dice is greater than $99\%$. Then, the least numerical value of $n$ is