All spades are removed from a well shuffled deck of 52 cards and then one card is drawn
randomly from the remaining cards. Find the probability of getting
(a) neither a heart nor a king
(b) neither an ace nor a king
(c) neither a red card nor a queen card
(d) a black card or an ace.
(e) either a heart or a spade card
(f) a red card
(g) a black card
(h) a spade card
(i) a diamond card
(j) a club card
(k) either an ace card or black card
(1) an ace card
(m)a face card with red colour
(n) neither '10' card nor an ace
(o) an even number card
(p) a face card
(q) an odd number card
Answers
(f)
let P(E) be the probability of finding a red card
P(E)=no of favourable outcomes
total no.of possible outcomes
Total no. of possible outcomes =52-13=39
No.of favourable outcomes=26
P(E)= 26 = 2
39 3
(g)
let P(E) be the probability of finding a black card
P(E)=no.of favourable outcomes
total no. of possible outcomes
Total no. possible outcomes =39
no.of favourable outcomes = 13
P(E)= 13 = 1
39 3
(h)
let P(E) be the probability of finding a spade card
P(E)=no.of favourable outcomes
total no. of possible outcomes
Total no. of possible outcomes=39
no.of favourable outcomes =0
P(E)=0
39
(i)
let P(E) be the probability of finding a diamond card
P(E)=no.of favourable outcomes
total no. of possible outcomes
no.of favourable outcomes = 13
total no. of possible outcomes=39
P(E)=13 = 1
39 3
(j)
let P (E) be the probability of finding a club card
p(e)=no.of favourable outcomes
total no. of possible outcomes
total no. of possible outcomes =39
no.of favourable outcomes=13
p(e)=13 =1
39 3
(k)
let P (E) be the probability of finding either an ace card or a black card
p(e)=no.of favourable outcomes
total no.of possible outcomes
total no.of possible outcomes =39
no.of favourable outcomes= 16
p(e)= 16
39
(l)
let P (E) be the probability of finding an ace card
p(e)=no.of favourable outcomes
total no.of possible outcomes
total no.of possible outcomes=39
no.of favourable outcomes=3
p(e)=3 =1
39 13
(m)
let P (E) be the probability of finding a face card with red colour
P (E)=no. of favourable outcomes
total no.of possible outcomes
p(e)=2
39
(n) let P E be the probability of finding neither 10 card or an ace
p(e)=2
13
(o)
p=5
13
p)
p(e)=3 by 13
q.4 by 39
