Two cards are drawn at random from a pack of 52 cards.what is the probability that either both are Red or both are king? A) 52/221 B) 55/190 C) 55/221 D) 19/221

 Two cards are drawn at random from a pack of 52 cards.what is the probability that either both are Red or both are king? A) 52/221 B) 55/190 C) 55/221 D) 19/221
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1 Answer

Answer :

Answer: C)

We have n(s) = 52C2 = 1326.

Let A = event of getting both red cards

B = event of getting both king

A∩B = event of getting king of red cards

n(A) = 26C2 = 325, n(B)= 4C2= 6 and n(A∩B) = 2C2 = 1

P(A) = n(A)/n(S) = 325/1326;

P(B) = n(B)/n(S) = 6/1326 and

P(A∩B) = n(A∩B)/n(S) = 1/1326

P(A∪B) = P(A) + P(B) - P(A∩B)

= (325+6-1) / 1326 = 330/1326 = 55/221
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Last Answer : Answer: B) Taking the individual probabilities of each number, getting a 4 is 1/6 and so is getting a 6. Applying the formula of compound probability, Probability of getting a 4 or a 6, P(4 or 6) = P(4) + P(6) – P(4 and 6) ==> 1/6 + 1/6 – 0 2/6 = 1/3

When a single die is rolled, the sample space is {1,2,3,4,5,6}.What is the probability of getting a 3 when a die is rolled? A) 1/2 B) 1/6 C) 6/1 D) 3/6

Description : When a single die is rolled, the sample space is {1,2,3,4,5,6}.What is the probability of getting a 3 when a die is rolled? A) 1/2 B) 1/6 C) 6/1 D) 3/6

Last Answer : Answer: B) No. of ways it can occur = 1 Total no. of possible outcomes = 6 So the probability of rolling a particular number (3) when a die is rolled = 1/6.

What is the channel capacity of a noisy channel with conditional probability of error p = 1/2?

Description : What is the channel capacity of a noisy channel with conditional probability of error p = 1/2? A) 0 B) 1 C) Infinity D) 2  

Last Answer : What is the channel capacity of a noisy channel with conditional probability of error p = 1/2?  A) 0 B) 1 C) Infinity D) 2  

Two cards are drawn from a well shuffled pack of 52 cards one after another without replacement. -Maths 9th

Description : Two cards are drawn from a well shuffled pack of 52 cards one after another without replacement. -Maths 9th

Last Answer : Probability of drawing an ace in the first draw = \(rac{4}{52}.\)Probability of drawing a queen of opposite shade in the second draw = \(rac{2}{51}.\)Probability of drawing a queen in the first draw = \(rac{4}{52}.\) ... \(rac{2}{51}\) = \(rac{4}{663}.\) [ AND' and OR'Theorems]

One card is drawn from a pack of 52 cards, each of the 52 cards being equally likely to be drawn. -Maths 9th

Description : One card is drawn from a pack of 52 cards, each of the 52 cards being equally likely to be drawn. -Maths 9th

Last Answer : (c) \(rac{1}{26}\)There is a total of 52 cards n(S) = 52 Let A : Event of drawing a red king Since there are only two red kings in the pack, n(A) = 2 ∴ P(A) = \(rac{2}{52}\) = \(rac{1}{26}\).

Four cards are drawn from a full pack of cards. Find the probability that : -Maths 9th

Description : Four cards are drawn from a full pack of cards. Find the probability that : -Maths 9th

Last Answer : 4 cards can be drawn from a pack of cards in 52C4 ways ∴ Exhaustive number of cases = n(S) = 52C4 (a) There are 4 suits, each containing 13 cards. Let A : Event of drawing one card from each suit ⇒ Favourable number of ... = \(rac{15229}{54145}\) (∵ P(Event) + P(complement of event) = 1)

There are three cards in a box. Both sides of one card are black, both sides of one card are red, and the third card has one black side and one red side. We pick a card at random and observe only one side. What is the probability that the opposite side is the same colour as the one side we observed? (A) 3/4 (B) 2/3 (C) 1/2 (D) 1/3

Description : There are three cards in a box. Both sides of one card are black, both sides of one card are red, and the third card has one black side and one red side. We pick a card at random and observe only one side. What is the ... the same colour as the one side we observed? (A) 3/4 (B) 2/3 (C) 1/2 (D) 1/3 

Last Answer : (B) 2/3

A bag contains 5 green and 7 red balls, out of which two balls are drawn at random. What is the probability that they are of the same colour ? -Maths 9th

Description : A bag contains 5 green and 7 red balls, out of which two balls are drawn at random. What is the probability that they are of the same colour ? -Maths 9th

Last Answer : (d) \(rac{31}{66}\)Total number of balls in the bag = 12 (5 Green + 7 Red) Let S be the sample space of drawing 2 balls out of 12 balls.Thenn(S) = 12C2 = \(rac{12 imes11}{2}\) = 66∴ Let A : Event of drawing two red balls⇒ ... \(rac{n(B)}{n(S)}\) = \(rac{21}{66}\) + \(rac{10}{66}\) = \(rac{31}{66}\).