Sample Question on Probability 02

 Sample Question on Probability 02

 

 

Question on Probability

 

A card is drawn at random from an ordinary deck of 52

playing cards . Find the probability that it is

(a) an ace

(b) a jack of hearts

(c) a three of clubs or a six of diamonds (d) a heart

(e) any suit except hearts

(f) a ten or a spade

(g) neither a four nor a club

 

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Answer

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For ease of understanding , let us take the following

considerations for respective events :

H = Hearts

S = Spade

D = Diamond

C = Club

1 = ace

11 = jack

12 = queen

13 = king

[2 ---- 9 ] as usual as on a deck of card .

 

Now lets find the answers to all sub-parts:

 

a) probability for finding an ace

=P(1 of each house)

=P(1nH or 1nC or 1nS or 1nD)

=P(1nH) + P(1nC) +P(1nD) + P(1nS)

=1/52 + 1/52 + 1/52 + 1/52

=4/52 = 1/13

 

(b) probability if finding a jack of hearts

=P(11 n H)

=1 / 52

 

(c) probability of getting a three of clubs or a 6 of

diamonds

=P(3 n C or 6 n D)

=P(3nC) + P(6nD)

=(1/52) + (1/52)

=1/26

 

(d) probability of getting a heart

=13/52

=1/4

 

(e) probability of getting any suit except hearts

=P(H')

=1 - P(H)

= 1 - 1/4

= 3/4

 

(f) probability of getting a 10 or a spade

= P( 10 U S)

= P(10) + P(S) - P(10 n S)

= (4/52) + (13/52) - (1/52)

= 16/52

= 4/13

 

(g) probability of getting neither a 4 nor a club

= P(4' U C')

= P(4') + P( C') - P( 4' n C')

= (48/52) + (39/52) - (36/52)

= 51/52