Question

one card is drawn from a pack of 52 cards. Find the probability of getting (i) a black card (ii)a face card (iii)black or queen (iv)either red or queen (v) neither red card nor a king (vi)jack and red card​

Answer 1

Answer:

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