Question -
Answer -
Given: Pack of 52cards.
By using the formula,
P (E) = favourableoutcomes / total possible outcomes
We know that, a cardis drawn from a pack of 52 cards, so number of elementary events in the samplespace is
n (S) = 52C1 =52
(i) Let E be theevent of drawing a black king
n (E) =2C1 =2(there are two black kings one of spade and other of club)
P (E) = n (E) / n (S)
= 2 / 52
= 1/26
(ii) Let E be theevent of drawing a black card or a king
n (E) = 26C1+4C1–2C1=28
[Weare subtracting 2 from total because there are two black king which are alreadycounted and to avoid the error of considering it twice.]
P (E) = n (E) / n (S)
= 28 / 52
= 7/13
(iii) Let E be theevent of drawing a black card and a king
n (E) =2C1 =2 (there are two black kings one of spade and other of club)
P (E) = n (E) / n (S)
= 2 / 52
= 1/26
(iv) Let E be theevent of drawing a jack, queen or king
n (E) = 4C1+4C1+4C1 =12
P (E) = n (E) / n (S)
= 12 / 52
= 3/13
(v) Let E be theevent of drawing neither a heart nor a king
Now let us consider E′as the event that either a heart or king appears
n (E′) = 6C1+4C1-1=16(there is a heart king so it is deducted)
P (E′) = n (E′) / n(S)
= 16 / 52
= 4/13
So, P (E) = 1 – P (E′)
= 1 – 4/13
= 9/13
(vi) Let E be theevent of drawing a spade or king
n (E)=13C1+4C1-1=16
P (E) = n (E) / n (S)
= 16 / 52
= 4/13
(vii) Let E be theevent of drawing neither an ace nor a king
Now let us consider E′as the event that either an ace or king appears
n(E′) = 4C1+4C1 =8
P (E′) = n (E′) / n(S)
= 8 / 52
= 2/13
So, P (E) = 1 – P (E′)
= 1 – 2/13
= 11/13
(viii) Let E be theevent of drawing a diamond card
n (E)=13C1=13
P (E) = n (E) / n (S)
= 13 / 52
= ¼
(ix) Let E be theevent of drawing not a diamond card
Now let us consider E′as the event that diamond card appears
n (E′) =13C1=13
P (E′) = n (E′) / n(S)
= 13 / 52
= 1/4
So, P (E) = 1 – P (E′)
= 1 – 1/4
= ¾
(x) Let E be theevent of drawing a black card
n (E) =26C1 =26 (spades and clubs)
P (E) = n (E) / n (S)
= 26 / 52
= ½
(xi) Let E be theevent of drawing not an ace
Now let us consider E′as the event that ace card appears
n (E′) = 4C1 =4
P (E′) = n (E′) / n(S)
= 4 / 52
= 1/13
So, P (E) = 1 – P (E′)
= 1 – 1/13
=12/13
(xii) Let E be theevent of not drawing a black card
n (E) = 26C1 =26 (red cards of hearts and diamonds)
P (E) = n (E) / n (S)
= 26 / 52
= ½