24. A card is selected from a pack of 52 parts calculate the probability that the card is
i) an Ace ii) a Black card.
Answers
Answer:
(a) When a card is selected from a pack of 52 cards the number of possible outcomes is 52 i.e., the sample space contains 52 elements
Therefore there are 52 points in the sample space
(b) Let A be the event in which the card drawn is an ace of spades
Accordingly n(A)=1. Since there is only one ace of spade in the deck.
∴P(A)=
Totalnumberofpossibleoutcomes
NumberofoutcomesfavourabletoA
=
n(S)
n(A)
=
52
1
(c) (i) Let E be the event in which the card drawn is an ace.
Since there are 4 aces in a pack of 52 cards n(E)=4
∴P(E)=
Totalnumberofpossibleoutcomes
NumberofoutcomesfavourabletoE
=
n(S)
n(E)
=
52
4
=
13
1
(ii) Let F be the event in which the card drawn is black
Since there are 26 black cards in a pack of 52 cards n(F)=26
∴P(F)=
Totalnumberofpossibleoutcomes
NumberofoutcomesfavourabletoF
=
n(S)
n(F)
=
52
26
=
2
1
(a) When a card is selected from a pack of 52 cards the number of possible outcomes is 52 i.e., the sample space contains 52 elements
Therefore there are 52 points in the sample space
(b) Let A be the event in which the card drawn is an ace of spades
Accordingly n(A)=1. Since there is only one ace of spade in the deck.
∴P(A)=
Totalnumberofpossibleoutcomes
NumberofoutcomesfavourabletoA
=
n(S)
n(A)
=
52
1
(c) (i) Let E be the event in which the card drawn is an ace.
Since there are 4 aces in a pack of 52 cards n(E)=4
∴P(E)=
Totalnumberofpossibleoutcomes
NumberofoutcomesfavourabletoE
=
n(S)
n(E)
=
52
4
=
13
1
(ii) Let F be the event in which the card drawn is black
Since there are 26 black cards in a pack of 52 cards n(F)=26
∴P(F)=
Totalnumberofpossibleoutcomes
NumberofoutcomesfavourabletoF
=
n(S)
n(F)
=
52
26
=
2
1