If a card is drawn from a pack of 52 cards. Find the probability of getting: (i) a black card (ii) not a black card (iii) a card bearing number between 2 to 5 including 2 and 5

8. If a card is drawn from a pack of 52 cards. Find the probability of getting:

(i) a black card

(ii) not a black card

(iii) a card bearing number between 2 to 5 including 2 and 5

Sol. There are 52 cards in a pack

∴  n (S) = 52

(i) Let A be event that the card drawn a black card

Total no. of black cards = 26

∴  n (A) = 26

P (A) = n (A)/n (S)

∴  P (A) = 26/52

∴  P (A) = ½

(ii) Let B be the event that the card drawn is not a black card

Total no. of red cards = 26

∴  n (B) = 26

P (B) = n (B)/n (S)

∴  P (B) = 26/52

∴  P (B) = ½

(iii)Let C be the event that card drawn bears number between 2 and 5 including 2 and 5

No. of cards between 2 and 5 including 2 and 5 is 4.

∴  There are 4 types of cards

∴  The total no. of cards between 2 and 5 including 2 and 5 is 4 × 4 = 16

n (C) = 16

P (C) = n (C)/n (S)

∴  P (C) = 16/52

∴  P (C) = 4/13