Q. 154.0( 23 Votes )

(i) E : ‘the card drawn is a spade’

F : ‘the card drawn is an ace’

(ii) E : ‘the card drawn is black’

F : ‘the card drawn is a king’

(iii) E : ‘the card drawn is a king or queen’

F : ‘the card drawn is a queen or jack’.

Answer :

Given: A deck of 52 cards.

(i) In a deck of 52 cards, 13 cards are spade and 4 cards are ace and only one card is there which is spade and ace both.

Hence, P(E) = The card drawn is a spade =

P(F) = The card drawn is an ace =

P(E ∩ F) = The card drawn is a spade and ace both = ..(1)

And P(E) . P(F)

..(2)

_{From (1) and (2)}

⇒ P (E ∩ F) = P(E) . P(F)

Hence, E and F are independent events.

(ii) In a deck of 52 cards, 26 cards are black and 4 cards are king and only two card are there which are black and king both.

Hence, P(E) = The card drawn is of black =

P(F) = The card drawn is a king =

P(E ∩ F) = The card drawn is a black and king both = ..(1)

And P(E) . P(F)

..(2)

_{From (1) and (2)}

⇒ P (E ∩ F) = P(E) . P(F)

Hence, E and F are independent events.

(iii) In a deck of 52 cards, 4 cards are queen, 4 cards are king and 4 cards are jack.

Hence, P(E) = The card drawn is either king or queen =

P(F) = The card drawn is either queen or jack =

There are 4 cards which are either king or queen and either queen or jack.

P(E ∩ F) = The card drawn is either king or queen and either queen or jack = ..(1)

And P(E) . P(F)

..(2)

_{From (1) and (2)}

⇒ P (E ∩ F) ≠ P(E) . P(F)

Hence, E and F are not independent events.

Rate this question :

How useful is this solution?

We strive to provide quality solutions. Please rate us to serve you better.

PREVIOUSProbability of solving specific problem independently by A and B are 1/2 and 1/3 respectively. If both try to solve the problem independently, find the probability that(i) the problem is solved (ii) exactly one of them solves the problem.NEXTIn a hostel, 60% of the students read Hindi newspaper, 40% read English newspaper and 20% read both Hindi and English newspapers. A student is selected at random.(a) Find the probability that she reads neither Hindi nor English newspapers.(b) If she reads Hindi newspaper, find the probability that she reads English newspaper.(c) If she reads English newspaper, find the probability that she reads Hindi newspaper

RELATED QUESTIONS :

Let A and B be the events such that

and

Find

(i) P(A ∩ B)

(ii) P(A ∪ B)

(iii) P(A / B)

RS Aggarwal - Mathematics

Mark the correct alternative in each of the following:

If A and B are two independent events such that P(A) = 0.3, P(A ∪ B) = 0.5, then P(A/B) – P(B/A) =

RD Sharma - Volume 2

Mark the correct alternative in each of the following:

If A and B are two independent events with then equals.

RD Sharma - Volume 2

Mark (√) against the correct answer in each of the following:

If A and B are two events such that P(A ∪ B) = , P(A ∩ B) = and P() = , then the events A and B are

RS Aggarwal - Mathematics

Mark (√) against the correct answer in each of the following:

If A and B are independent events, then P=?

RS Aggarwal - Mathematics

Mark (√) against the correct answer in each of the following:

If P(A) = , P(B) = and P(A ∩ B) = , then P(= ?

RS Aggarwal - Mathematics

Mark the correct alternative in each of the following:

If the events A and B are independent, then P(A ∩ B) is equal to

RD Sharma - Volume 2

Mark (√) against the correct answer in each of the following:

If P(A) = , P(B) = and P(A ∪ B) = , then P(A/B)=?

RS Aggarwal - Mathematics

If A and B are two independent events such that =2/15 and =1/6, then find P(B).

RD Sharma - Volume 2