Question

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​

Answer 1

⇒ 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:

$\bf{\longrightarrow\:P(Outcome\:1)=0}$

(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

$\sf{P(Outcome\:2)=\dfrac{Favourable\:events}{Total\:events}}$

$\sf{P(Outcome\:2)=\dfrac{20}{40}}$

$\bf{\longrightarrow\:P(Outcomes\:2)=\dfrac{1}{2}}$

(iii) a black ace

No. of black ace cards = 2

Total no. of cards = 40

$\sf{P(Outcome\:3)=\dfrac{Favourable\:events}{Total\:events}}$

$\sf{P(Outcome\:3)=\dfrac{2}{40}}$

$\bf{\longrightarrow\:P(Outcome\:3)=\dfrac{1}{20}}$