point between the pillars and the height of each pillar.
33. All jacks, queens and kings are removed from a pack of 52 cards. The remaining cards are well shuffled
and then a card is randomly drawn from it. Find the probability that this card is:
(i) a black face card
(ii) a red card
(iii) a black ace
⇒ Given:
A deck of 52 cards with all the jacks, kings and queens removed.
⇒ To Find:
The probability of randomly drawing:
(i) a black face card
(ii) a red card
(iii) a black ace
from the rest of the cards.
⇒ Solution:
➡ The number of jacks in a deck = 4 [one each from spade, club, diamond and heart]
➡ The number of kings in a deck = 4 [one each from spade, club, diamond and heart]
➡ The number of queens in a deck = 4 [one each from spade, club, diamond and heart]
Total number of cards removed = 4 x 3 = 12
Remaining cards = 52 – 12 = 40 cards
Now, solving the questions:
(i) a black face card
The black faced cards in the deck were the king, queen and the jack which were removed.
Hence:
[tex]\bf{\longrightarrow\:P(Outcome\:1)=0}[/tex]
(ii) a red card
The total number of red cards is 26 (13 x 2).
From this, we need to subtract 6 cards – the three face cards from each set.
That is:
26 – 6 = 20
[tex]\sf{P(Outcome\:2)=\dfrac{Favourable\:events}{Total\:events}}[/tex]
[tex]\sf{P(Outcome\:2)=\dfrac{20}{40}}[/tex]
[tex]\bf{\longrightarrow\:P(Outcomes\:2)=\dfrac{1}{2}}[/tex]
(iii) a black ace
No. of black ace cards = 2
Total no. of cards = 40
[tex]\sf{P(Outcome\:3)=\dfrac{Favourable\:events}{Total\:events}}[/tex]
[tex]\sf{P(Outcome\:3)=\dfrac{2}{40}}[/tex]
[tex]\bf{\longrightarrow\:P(Outcome\:3)=\dfrac{1}{20}}[/tex]