A card is drawn at random form a well _shuffeled pack of 52 cards what is probability of getting a) a black card B) no heart C) a king
Answers
Answer:
king
Step-by-step explanation:
ans is king
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No. of cards in a pack =52
Solution(i):
No. of black kings =2
Therefore,
2
C
1
( Selecting 1 out of 2 items) times out of
52
C
1
( Selecting 1 out of 52 items) a black king is picked.
Let E be the event of getting a black king from pack
We know that, Probability P(E) =
(Total no.of possible outcomes)
(No.of favorable outcomes)
=
52
C
1
2
C
1
=
52
2
=
26
1
Solution(ii):
No. of black cards or kings =28..... (26Black(including 2 Black kings) + 2 Red Kings)
Therefore,
28
C
1
( Selecting 1 out of 28 items) times out of
52
C
1
( Selecting 1 out of 52 items) a either a black card or a king is picked.
Let E be the event of getting either a black card or a king from pack
We know that, Probability P(E) =
(Total no.of possible outcomes)
(No.of favorable outcomes)
=
52
C
1
28
C
1
=
52
28
=
13
7
Solution(iii):
No. of jack, queen or king =12 (4- Jack, 4- Queen, 4-King)
Therefore,
12
C
1
( Selecting 1 out of 12 items) times out of
52
C
1
( Selecting 1 out of 52 items) a jack, queen or a king is picked.
Let E be the event of getting a jack, queen or a king from pack
We know that, Probability P(E) =
(Total no.of possible outcomes)
(No.of favorable outcomes)
=
52
C
1
12
C
1
=
52
12
=
13
3
Solution(iv):
No. of spade or ace =16 ........(13-Spade(including 1-Ace) + 3-Aces)
Therefore,
16
C
1
( Selecting 1 out of 16 items) times out of
52
C
1
( Selecting 1 out of 52 items) a spade or an ace is picked.
Let E be the event of getting a spade or an ace from pack
We know that, Probability P(E) =
(Total no.of possible outcomes)
(No.of favorable outcomes)
=
52
C
1
16
C
1
=
52
16
=
13
4
Solution(v):
No. of neither ace nor king =52−8=44 ...... (As there are 4-Kings and 4-Aces)
Therefore,
44
C
1
( Selecting 1 out of 44 items) times out of
52
C
1
( Selecting 1 out of 52 items) a neither an ace nor a king is picked.
Let E be the event of getting neither an ace nor a king from pack
We know that, Probability P(E) =
(Total no.of possible outcomes)
(No.of favorable outcomes)
=
52
C
1
44
C
1
=
52
44
=
13
11
Solution(vi):
No. of neither red nor queen $$=52-28=24$$ ...(26-red+ 2-Black Queen)
Therefore,
24
C
1
( Selecting 1 out of 24 items) times out of
52
C
1
( Selecting 1 out of 52 items) neither red nor a queen is picked.
Let E be the event of getting neither red nor queen from pack
We know that, Probability P(E) =
(Total no.of possible outcomes)
(No.of favorable outcomes)
=
52
C
1
24
C
1
=
52
24
=
13
6
Solution(vii):
No. of non-ace cards =52−4= 48 ......(4 Aces)
Therefore,
48
C
1
( Selecting 1 out of 48 items) times out of
52
C
1
( Selecting 1 out of 52 items) non-ace card is picked.
Let E be the event of getting a non-ace card from pack
We know that, Probability P(E) =
(Total no.of possible outcomes)
(No.of favorable outcomes)
=
52
C
1
48
C
1
=
52
48
=
13
12