Suppose that each child born is equally likely to be a boy or a girl. Consider a family with exactly three children.
List the eight elements in the sample space whose outcomes are all possible genders of the three children.

2

(a)

A and B are two events that P(A) = 0.54, P(B) = 0.69 and \(P(A\cap B)\) = 0.35. Find \(P(B\cap A')\)

2

(a)

The probability that at least one of the events A and B occurs is 0.6. If A and B occurs simultaneously with probability 0.2, then find \(P(\overline { A } )+P(\overline { B } ).\)

2

(a)

One urn contains two black balls (labelled B₁ and B₂) and one white (W) ball. A second urn contains one black (B) ball and two white balls (labelled W₁ and W₂ ). Suppose the following experiment is performed.
One of the two urns is chosen at random. Next , a ball is randomly chosen from the urn. Then, a second ball is chosen at random from the same urn without replacing the first ball. What is the probability that two balls of opposite colour are chosen?

2

(a)

If A and B are two events having \(P(A\cup B)=\frac { 1 }{ 2 } \ and\ P(\overline { A } )=\frac { 2 }{ 3 } ,\ then\ find\ P(\overline { A } \cap B).\)

2

(a)

While suffling a pack of 52 playing cards, 2 are accidentally dropped. Find the probability that the missing cards to be of different colours.

2

(a)

If the letters of the word ALGORITHM are arranged at random in a row, what is the probability the letters GOR must remain together as a unit?

2

(a)

A single letter is selected at random from the word 'PROBABILITY', then find the probability that letter is vowel. 

2

(a)

Three digit numbers are formed using the digits 0,2,4,6,8.A number is chosen at random out of these numbers.What is the probability that this number has the same digits?

2

(a)

A card is drawn from a deck of 52 cards. Find the probability of getting a king or a heart or a red card.

2

(a)