Question

7) i) Two cards are drown from a standard deck of 52 playing
cards one after another with replacement. What is the probability
the both the cards are face cards?
a)
b) 109 c)
d) e) None of these
ii) Two cards are drowned from a standard deck of 52 playing
cards one after another without replacement. What is the
probability the both the cards are black cards?
27
25
31
a) b)
d) 2012 e) None of these
169
169
a) 102 b
c)
102
102​

Answer 1

Given:

A pack of 52 cards.

Two cards are drawn.

Solution:

(i) Two cards are drawn one after another with replacement. Probability that the both the cards are face cards?

A deck of 52 cards contains 12 face cards:

4 King, 4 Queen, 4 Jack

Probability of getting a face card = 12/52

ATQ

Two cards are drawn one after the other, with replacement.

Probability of drawing a face card first time = 12/52

Probability of drawing a face card second time = 12/52

Probability that both the cards drawn are face cards = 12/52 x 12/52 = 9/169

Hence, the probability that both the cards drawn are face cards is 9/169.

(ii) Two cards are drawn one after another without replacement. Probability that the both the cards are black cards?

A deck of 52 cards contains 26 black cards

Probability of getting a black card = 26C1/52C1

After drawing one black card, remaining cards are 51 and 25 black cards

Probability of getting other black card =25C1/51C1

Probability of getting both black cards

= 26C1/52C1 × 25C1/51C1

= 26/52 × 25/51

= 25/102

Hence, the probability that two black cards are drawn is 25/102.

Answer 2

Step-by-step explanation:

Given: -

• Two cards are drown from a standard deck of 52 playing

• cards one after another with replacement.

Solution: ( 1 )

To Find : -

• What is the probability the both the cards are face cards?

A deck of 52 cards contains 12 face cards:

= 12/52

Probability that both the cards drawn are face cards

= 12/52 x 12/52

= 3/ 13 × 3/13

= 9/169

________________________

Solution ( 2 )

To Find : -

• What is the probability the both the cards are black cards?

Solution : -

A deck of 52 cards contains 26 black cards

26C_1/52C_1

Probability of getting other black card = 25C_1/51C_1

= 26C_1/52C_1 × 25C_1/51C_1

= 1/2 × 1/51

= 25/102

_____________________________

More Information : -

probability means the quality or state of being probable; the extent to which something is likely to happen or be the case.

• Probability is a branch of mathematics that deals with calculating the likelihood of a given event's occurrence.

• which is expressed as a number between 1 and 0. An event with a probability of 1 can be considered a certainty:

For example : - the probability of a coin toss resulting in either "heads" or "tails" is 1, because there are no other options, assuming the coin lands flat.

• An event with a probability of .5 can be considered to have equal odds of occurring or not occurring: for example, the probability of a coin toss resulting in "heads" is .5,

• because the toss is equally as likely to result in "tails." An event with a probability of 0 can be considered an impossibility: