All the black face cards are removed from a pack of 52 cards. The remaining cards are well shuffled and then a card is drawn at random. Find the probability of getting
(i)face card
(ii)red card
(iii)black card
(iv)king
Answers
SOLUTION:
Given : All the black face cards are removed from a pack of 52 cards .
King, queen ,and jack are called face cards.
2 black Kings, 2 black queen and 2 black jack are removed from the Deck of 52 playing cards.
So, remaining cards in deck = 52 - 6 = 46
Total number of outcomes = 46
(i) We know ,that there are 12 face cards.
6 black face cards are removed.
Remaining face cards = 12 - 6 = 6
Let E1 = Event of getting a face card
Number of favourable outcomes to E1= 6
Required probability P(E1)= Number of favourable outcomes / total number of outcomes
P(E1) = 6/46 = 3/23
Hence, the Required probability of getting a face card , P(E1) = 13/46
ii) We know ,that there are 26 red cards in a deck.
Let E2 = event of getting a red card
Number of favourable outcomes to E2 = 26
Probability P(E2) = Number of favourable outcomes / total number of outcomes
P(E2) = 26/46 = 13/23
Hence, the Required probability of getting a red card, P(E2) = 13/23
(iii) We know, that there are 26 black cards in a Deck .6 black face cards are removed Remaining black cards are = 26 - 6 = 20
Let E3 = Event of getting a black card
Number of favourable outcomes to E3 = 20
Required probability P(E3) = Number of favourable outcomes / total number of outcomes
P(E3) = 20/46 = 10/23
Hence, the Required probability of getting a black card, P(E3) = 10/23 .
(iv) We know ,that there are (2 black + 2 red) 4 king cards in a deck. 2 black kings are removed.
Remaining king card left = 4 - 2 = 2
Let E4 = Event of getting a king card
Number of outcome favourable to E4 = 2
Probability (E4) = Number of favourable outcomes / Total number of outcomes
P(E4) = 2/46 = 1/23
Hence, the required probability of getting a king card , P(E4) = 1/23.
HOPE THIS ANSWER WILL HELP YOU….
Answer:
ANSWER
Given that
Total Card =52
Part (1)
Probability of Face card =
52
12
=
13
3
Part (2)
Probability of neither a king nor a red
Card =
52
28
=
13
7
Hence, this is the answer.