Question

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
​


Solution(viii):
No. of cards with no. 10 =4
Therefore,
4
C
1
​
( Selecting 1 out of 4 items) times out of
52
C
1
​
( Selecting 1 out of 52 items) card with no. 10 is picked.

Let E be the event of getting a card with no. 10 from pack

We know that, Probability P(E) =
(Total no.of possible outcomes)
(No.of favorable outcomes)
​
=
52
C
1
​

4
C
1
​

​
=
52
4
​
=
13
1
​


Solution(ix):
No. of spade cards =13
Therefore,
13
C
1
​
( Selecting 1 out of 13 items) times out of
52
C
1
​
( Selecting 1 out of 52 items) a spade card is picked.

Let E be the event of getting a spade card from pack

We know that, Probability P(E) =
(Total no.of possible outcomes)
(No.of favorable outcomes)
​
=
52
C
1
​

13
C
1
​

​
=
52
13
​
=
4
1
​


Solution(x):
No. of black cards =26
Therefore,
26
C
1
​
( Selecting 1 out of 26 items) times out of
52
C
1
​
( Selecting 1 out of 52 items) a black card is picked.

Let E be the event of getting a black card from pack

We know that, Probability P(E) =
(Total no.of possible outcomes)
(No.of favorable outcomes)
​
=
52
C
1
​

26
C
1
​

​
=
52
26
​
=
2
1
​


Solution(xi):
No. of seven of clubs =1
Therefore,
1
C
1
​
( Selecting 1 out of 1 items) times out of
52
C
1
​
( Selecting 1 out of 52 items) a seven of clubs is picked

Let E be the event of getting a seven of clubs from the pack

We know that, Probability P(E) =
(Total no.of possible outcomes)
(No.of favorable outcomes)
​
=
52
C
1
​

1
C
1
​

​
=
52
1
​
=
52
1
​


Solution(xii):
No. of jacks =4
Therefore,
4
C
1
​
( Selecting 1 out of 4 items) times out of
52
C
1
​

Answer 1

Answer:

what ever... thank you for the free points