Probability

Probability for Heads = probability for tails = 1/2 and each trial is independent. Hence required probability= 1/21/21/2 = 1/8.

Probability of 1st ball red = 6/16 and probability of 2nd blue ball = 7/15

Favourable outcomes are 6 and total are 36. Hence, 1/6 is right.

Probability = 4(3)/52C2 = 4/663; right answer.

There are 4 queens, hence the answer is ⁴C₃/⁵²C₃

Right answer; favourable outcomes are 1,2...6. Hence 6/36.

For not a sunday probability = 1- probability for 53 sundays= 1-2/7 = 5/7.

Number of kings = 4. Hence probability = 4/52.

Probability = (5C2)(4C2)/9C4 = 60/126 = 10/21

Number of kings is a binomial with p = 1/13P(x=1) = 5C1(1/13)(12/13)^4= 3243/10829.

Correct; np =4 npq = 2, q =p = 1/2 and n = 8. Hence, the answer is 8C2(0.5)^8.

Either 4 heads and one tail in the fourth or 4 tails and 4 heads. Probability = 2(0.5)^5 = 1/16 = 1/4x which gives x = 4.

Probability that both speak truth or that both speak false= (0.6)(0.5) +(0.4)(0.5) =0.5.

The first die can show any numbers from 1 of 6. Second can show numbers greater than the first and third acn show greater than the second. Number of ways = (1,2,3) (1,2,4)(1,2,5)(1,2,6) (1,3,6) (1,4,6) (1,3,5) (1,4,5) (1,4,6)(1,5,6), (2,3,6) (2,3,5)(2,3,4) (2,4,5) (2,4,6) (2,5,6) (3,4,5) (3,4,6) (3,5,6) (4,5,6). Hence, probability = 20/216 = 5/54.

Probability for 5 to be placed in the correct colour = ⁿC_r P^r Q ^{n - r}
P = 1/8, Q = 7/8
= 8C5(1/8)^5(7/8)^3 = 1/360