All the jacks, queensapd 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 x 4 = 40.
(i) Let $E_{1}=$ 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
$\therefore \quad n\left(E_{1}\right)=4$
$\therefore \quad P\left(E_{1}\right)=\frac{n\left(E_{1}\right)}{n(S)}=\frac{4}{40}=\frac{1}{10}$
(ii) Let $E_{2}=$ Event of getting a card whose value is greater than 7
$=$ Event of getting a card whose value is 8,9 or 10
$\therefore \quad n\left(E_{2}\right)=3 \times 4=12$
$P\left(E_{2}\right)=\frac{n\left(E_{2}\right)}{n(S)}=\frac{12}{40}=\frac{3}{10}$
(iii) Let $E=$ 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
$\therefore \quad n\left(E_{3}\right)=6 \times 4=24$
$\therefore \quad P\left(E_{3}\right)=\frac{n\left(E_{3}\right)}{n(S)}=\frac{24}{40}=\frac{3}{5}$