Consider an event with probability of success `1/2.`If there are n trails then probability of getting successes where `r=4k,k in z` is

Consider an event for which probability of success is . Statement 1: Probability than in n trials, there are r successes where r=4k and k is an integer is 1/4+1/(2^(n//2+1))cos((npi)/4) Statement 2: .^n C_0+^n C_4+^n C_8......... =2^(n//2)sin((npi)/4) .

If there are n independent trials, p and q are the probability of success and failure respectively, then probability of exactly r success

If there are n independent trials, p and q are the probability of success and failure respectively, then probability of exactly r success

If there are n independent trials, p and q are the probability of success and failure respectively, then probability of exactly r success

A fair die is thrown thrice. Getting l or 6 is considered as a success. i. Find p and q, the probability of success and failure respectively in any one trial. ii. Obtain the probability distribution of the successes.

A die is tossed thrice. If event of getting an even number is a success. Then the probability of getting at least two successes is

A coin is tossed 4 times. If getting a tail is a success, then the probability of 3 successes is :