All the jacks, queens and kings are removed from a deck of 52 playing cards. The remaining cards are well shuffled and then one card is drawn at random. Giving ace a value 1 similar value for other cards, find the probability that the card has a value.
(i) 7
(ii) greater than 7
(iii) less than 7
In out of 52 playing cards, 4 jacks, 4 queens and 4 kings are removed, then the remaining cards are left,
n(S) = 52 - 3×4 = 40
(i) Let E1 = Event of getting a card whose value is 7
E = Card value 7 may be of a spade, a diamond, a club or a heart
∴ n(E1) = 4
(ii) Let E2 = Event of getting a card whose value is greater than 7
= Event of getting a card whose value is 8, 9 or 10
(E2)
(iii) Let E3 = Event of getting a card whose value is less than 7
= Event of getting a card whose value is 1, 2, 3, 4, 5 or 6
∴ n(E3) = 6×4 = 24
