Red queens and black jacks are removed from a pack of 52 playing cards. A card is drawn at random from the remaining cards, after reshuffling them. Find the probability that the drawn card is 1. a king. 2. of red colour. 3. a face card. 4. a queen.
Answers
Answer:
Total no. of cards in pack =52
After removing red queens(2), and black jacks(2)
No. of cards =52−4=48
Solution(i):
No. of kings =4
Therefore,
4
C
1
( Selecting 1 out of 4 items) times out of
48
C
1
( Selecting 1 out of 48 items) a king is picked.
Let E be the event of getting a king from pack
We know that, Probability P(E) =
(Total no.of possible outcomes)
(No.of favorable outcomes)
=
48
C
1
4
C
1
=
48
4
=
12
1
Solution(ii):
No. of red colors =26−2=24......(2 red queen cards already drawn)
Therefore,
24
C
1
( Selecting 1 out of 24 items) times out of
48
C
1
( Selecting 1 out of 48 items) a red is picked.
Let E be the event of getting red from the pack
We know that, Probability P(E) =
(Total no.of possible outcomes)
(No.of favorable outcomes)
=
48
C
1
24
C
1
=
48
24
=
2
1
Solution(iii):
No. of face cards =8 ....... (2 red queen, 2 black jack (face cards) already drawn)
Therefore,
8
C
1
( Selecting 1 out of 8 items) times out of
48
C
1
( Selecting 1 out of 48 items) a face card is picked.
Let E be the event of getting a face card from the pack
We know that, Probability P(E) =
(Total no.of possible outcomes)
(No.of favorable outcomes)
=
48
C
1
8
C
1
=
6
1
Solution(iv):
No. of queen cards =4−2=2...(2 red queen cards already drawn)
Therefore,
2
C
1
( Selecting 1 out of 2 items) times out of
48
C
1
( Selecting 1 out of 48 items) a queen is picked.
Let E be the event of getting a queen from the pack
We know that, Probability P(E) =
(Total no.of possible outcomes)
(No.of favorable outcomes)
=
48
C
1
2
C
1
=
24
1
I hope it is helpful to you!!