Question

QUESTION
___________________________


A card from a pack of 52 cards is lost. From the remaining cards of the pack, two cards are drawn and are found to be both diamonds. Find the probability of the lost card being a diamond.


____________________________

Harsh Pratap Singh ​

Answer 1

Answer:

ANSWER

Let E

1

be the event that the lost card is Diamond

Given that there are 13 diamonds in the deck P(E

1

)=

52

13

=

4

1

let E

2

be the even that the lost card is not a diamond P(E

2

)=

4

3

Let A be the event that the two cards drawn are both diamonds

P(A/E

1

)=

51

C

1

12

C

2

=

Totalno.ofwaysofdrawing2cards

No.ofwaysofdrawing2diamondscards

=

1275

66

P(A/E

2

)=

51

C

2

13

C

2

=

1275

78

Applying Bayes Theorem, where

P(E

1

/A)=

P(E

1

)×P(A/E

1

)+P(E

2

)×P(A/E

2

)

P(E

1

)×(P(A/E

1

))

=

1275

66

×

4

1

+

1275

78

×

4

3

1275

66

×

4

1

=

50

11

Answer 2

Step-by-step explanation:

refer to the attachment above ♡