Question

A card is drawn at random from a well shuffled pack of 52 playing cards. Find the probability that the drawn card is neither a jack nor an ace.​

Answer 1

$\huge{\underline{\mathtt{\red{A}\pink{N}\green{S}\blue{W}\purple{E}\orange{R}}}}$

Total number of cards = 52

Numbers of jacks = 4

Numbers of aces = 4

Card is neither a jack nor an ace

= 52 – 4 – 4 = 44

∴ Required probability = 44/52=11/13

Answer 2

$\Large{\underbrace{\underline{\bf{QUESTION\:}}}}:$

A card is drawn at random from a well shuffled pack of 52 playing cards. Find the probability that the drawn card is neither a jack nor an ace.

$\Large{\underbrace{\underline{\bf{ANSWER\:}}}}:$

${\bf{Given\::}}$

• A card is drawn at random from a well shuffled pack of 52 playing cards.

$\\ {\bf{To\: Find\::}}$

• The probability that the drawn card is neither a jack nor an ace.

$\\ {\bf{Solution\::}}$

★ As we all know that a deck of playing cards contains 52 cards, and here the set of these cards is our sample space, therefore the number of sample spaces will become 52.

Therefore,

➵ Total number of cards = n(S) = 52

$\Large{\underline{\underline{\bf{CONCEPT\:}}}}:$

★ As we all know there are four types of cards in a deck namely,

1. Hearts
2. Clubs
3. Diamonds
4. Spades

★ And they all contain equal numbers of cards in the deck.

Therefore,

✯ Total number of Hearts/Clubs/Diamonds/Spades are,

$:\implies\:\tt{\dfrac{52}{4}\:}$

$:\implies\:\tt{13\:}$

★ Also, each set has one Ace. As there are four sets therefore each one will contain one Ace, i.e. we have a total four Aces.

Now, come back to this problem.

☛ Here we have to find the probability that a card drawn is neither a jack nor an Ace.

Let,

• ‘A’ be the set of conditions given above.

★ As we all know that the deck of cards has four sets of each card. Therefore there are 4 jacks and 4 Aces are there in a deck.

★ As we want a condition where both jack and ace are not required therefore we have to subtract them from the total number of cards.

Therefore,

✯ Number of cards with neither jack or ace

$\longrightarrow\:\tt{52\: - \:(4 \:+ \:4)}$

$\longrightarrow\:\tt{52\: - \:8}$

$\longrightarrow\:\tt{44}$

Therefore,

✯ Number of cards with neither jack or ace = 44

➵ n(C) = 44

As we know that,

$\orange\bigstar\:{\huge\mid}\:\bf\purple{P(E)\:=\:\dfrac{n(C)}{n(S)}\:}{\huge\mid}\:\green\bigstar$

➳ P(A) = $\tt{\dfrac{44}{52}}$

➳ P(A) = $\tt{\dfrac{22}{26}}$

➳ P(A) = $\bf\pink{\dfrac{11}{13}}$