Question

All the jacks, queens and kings are removed from a deck of 52 playing cards. The remaining cards as well shuffled and then one card is drawn at random. Giving ace a value 1 similar value for other fards, find the probability that the card has a value.
(i) 7 (ii) Greater than 7
(iii) less than 7

Answer 1

In out of 52 playing cards, 4 jacks, 4 queens and 4 kings are removed, then the remaining cards are left, n(s)=`52-3xx4=40`
(i) Let `E_(1)`=Event of getting a card whose value is 7
E=Card value 7 may be of a spadem a diamond, a club or a heart
`n(E_(1))=4`
`therefore P(E_(1))=(n(E_(1)))/(n(S))=(4)/(40)=(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 n(E_(2))=3xx4=12`
`therefore P(E_(2))=(n(E_(2)))/(n(S))=(12)/(40)=(3)/(10)`
(iii) Let `E_(3)`=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 n(E_(3))=6xx4=24`
`therefore P(E_(3))=(n(E_(3)))/(n(S))=(24)/(40)=(3)/(10)`