1) 1 card is drawn, what is the probability that, 1 card is CLUB .
Solution:
Total number of ways of drawing 1 cards from 52 cards
`n(S) = 52`
Let `E` = event of getting 1 card is club
Total number of club cards = 13
Hence, `n(E)=` number of ways of drawing 1 club from 13
`n(E) = 13`
`:.P(E)=(n(E))/(n(S))=13/52=1/4`
2) 1 card is drawn, what is the probability that, 1 card is FACE Card .
Solution:
Total number of ways of drawing 1 cards from 52 cards
`n(S) = 52`
Let `E` = event of getting 1 card is face card
Total number of face card cards = 16
Hence, `n(E)=` number of ways of drawing 1 face card from 16
`n(E) = 16`
`:.P(E)=(n(E))/(n(S))=16/52=4/13`
3) 1 card is drawn, what is the probability that, 1 card is QUEEN .
Solution:
Total number of ways of drawing 1 cards from 52 cards
`n(S) = 52`
Let `E` = event of getting 1 card is queen
Total number of queen cards = 4
Hence, `n(E)=` number of ways of drawing 1 queen from 4
`n(E) = 4`
`:.P(E)=(n(E))/(n(S))=4/52=1/13`
4) 1 card is drawn, what is the probability that, 1 card is QUEEN or 1 card is KING
Solution:
Total number of ways of drawing 1 cards from 52 cards
`n(S) = 52`
Let `E` = event of getting 1 card is queen or king
Total number of queen cards = 4
Total number of king cards = 4
Hence, `n(E)=` number of ways of drawing 1 queen from 4 or 1 king from 4
`:. n(E)={::}^4 C_1+{::}^4 C_1=4+4=8`
`:.P(E)=(n(E))/(n(S))=8/52=2/13`
5) 2 card is drawn, what is the probability that, 1 card is RED and 1 card is KING
Solution:
Total number of ways of drawing 2 cards from 52 cards
`n(S) = {::}^52 C_2=1326`
Let `E` = event of getting 1 card is red and 1 card is king
Total number of red cards = 26
Total number of king cards = 4
Hence, `n(E)=` number of ways of drawing 1 red from 26 or 1 king from 4
`:. n(E)={::}^26 C_1xx{::}^4 C_1=26 xx 4=104`
`:.P(E)=(n(E))/(n(S))=104/1326=4/51`
6) 2 card is drawn, what is the probability that, 2 card is RED or 2 card is KING
Solution:
Total number of ways of drawing 2 cards from 52 cards
`n(S) = {::}^52 C_2=1326`
Let `E` = event of getting 2 card is red or 2 card is king
Total number of red cards = 26
Total number of king cards = 4
Total number of cards which are both red and king=2
Hence, `n(E)=` number of ways of drawing 2 red from 26 or 2 king from 4
`:. n(E)={::}^26 C_2+{::}^4 C_2-{::}^2 C_2=325+6-1=330`
`:.P(E)=(n(E))/(n(S))=330/1326=55/221`
7) 2 card is drawn, what is the probability that, 2 card is FACE Card .
Solution:
Total number of ways of drawing 2 cards from 52 cards
`n(S) = {::}^52 C_2=1326`
Let `E` = event of getting 2 card is face card
Total number of face card cards = 16
Hence, `n(E)=` number of ways of drawing 2 face card from 16
`n(E) = {::}^16 C_2=120`
`:.P(E)=(n(E))/(n(S))=120/1326=20/221`
This material is intended as a summary. Use your textbook for detail explanation.
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