Last visit was: 06 Oct 2024, 02:10 It is currently 06 Oct 2024, 02:10
Decision Tracker
My Rewards
Unanswered
Active Topics
New posts
New comers' posts
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

One card is drawn at random from a pack of 52 cards. What is the proba

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
avatar
B
KANNUPRIYA17
Joined: 12 May 2020
Posts: 9
Own Kudos [?]: 11 [5]
Given Kudos: 28
Location: India
Send PM
One card is drawn at random from a pack of 52 cards. What is the proba [#permalink] One card is drawn at random from a pack of 52 cards. What is the proba   15 Dec 2021, 03:13
5
Bookmarks
00:00
A
B
C
D
E

Difficulty:

55% (hard)

Question Stats:

63% (01:54) correct 37% (02:06) wrong based on 73 sessions
Hide Show DIFFICULTY AND TIMER STATISTICS
One card is drawn at random from a pack of 52 cards. What is the probability that the card drawn is NEITHER a 'spade' NOR a'10' NOR a'Red'.


A.9/52

B.3/13

C.10/13

D.21/26

E.43/52
ShowHide Answer
Official Answer
B
User avatar
P
Regor60
Joined: 21 Nov 2021
Posts: 483
Own Kudos [?]: 265 [2]
Given Kudos: 394
Send PM
Re: One card is drawn at random from a pack of 52 cards. What is the proba [#permalink] One card is drawn at random from a pack of 52 cards. What is the proba   15 Dec 2021, 15:35
2
Kudos
Not a red leaves just clubs and spades.

Not a spade just leaves clubs.

Not a 10 leaves 12 remaining clubs

12/52=3/13

Posted from my mobile device
avatar
B
D33T
Joined: 27 Nov 2021
Posts: 19
Own Kudos [?]: 30 [0]
Given Kudos: 95
Send PM
Re: One card is drawn at random from a pack of 52 cards. What is the proba [#permalink] One card is drawn at random from a pack of 52 cards. What is the proba   15 Dec 2021, 21:06
Can someone help review my working method and help identify what I'm doing wrongly? I used the following approach but couldn't reach any of the answer choices.

In any given deck of 52 cards, there are:
Red = 26 cards --> Prob: 26/ 52 (i.e. 1/2)
'10' = 4 cards --> Prob: 4/52
Spades = 13 cards --> Prob: 13/52 (i.e. 1/4)

Probabilities of picking a single card with the following characteristics are:
Black (i.e. not red) = 1/2
'1-9, JQK' (i.e. not '10') = 48/52
Hearts, Clubs, Diamonds (i.e. not Spades) = 39/52 = 3/4

Therefore:
Prob (not red AND not '10' AND not spade) = 1/2 * 48/52 * 3/4 = 9/26
User avatar
P
Regor60
Joined: 21 Nov 2021
Posts: 483
Own Kudos [?]: 265 [2]
Given Kudos: 394
Send PM
Re: One card is drawn at random from a pack of 52 cards. What is the proba [#permalink] One card is drawn at random from a pack of 52 cards. What is the proba   16 Dec 2021, 04:16
2
Kudos
D33T
Can someone help review my working method and help identify what I'm doing wrongly? I used the following approach but couldn't reach any of the answer choices.

In any given deck of 52 cards, there are:
Red = 26 cards --> Prob: 26/ 52 (i.e. 1/2)
'10' = 4 cards --> Prob: 4/52
Spades = 13 cards --> Prob: 13/52 (i.e. 1/4)

Probabilities of picking a single card with the following characteristics are:
Black (i.e. not red) = 1/2
'1-9, JQK' (i.e. not '10') = 48/52
Hearts, Clubs, Diamonds (i.e. not Spades) = 39/52 = 3/4

Therefore:
Prob (not red AND not '10' AND not spade) = 1/2 * 48/52 * 3/4 = 9/26

When multiplying probabilities you are saying both events are occurring.

Once you've established black in your first statement, red should be eliminated in your third. The third statement should read "clubs" 1/2, indicating a further partitioning of black from the first statement

Posted from my mobile device
avatar
B
D33T
Joined: 27 Nov 2021
Posts: 19
Own Kudos [?]: 30 [1]
Given Kudos: 95
Send PM
Re: One card is drawn at random from a pack of 52 cards. What is the proba [#permalink] One card is drawn at random from a pack of 52 cards. What is the proba   16 Dec 2021, 05:11
1
Bookmarks
Thanks so much! Regor60
Applying that approach, the probabilities work out to be -

Black (only clubs or spades): 26/52 (ie 1/2)
Not 10 (1-9, JQK): (26-2)/26 (ie 12/13)
Not Spade: 12/24 (ie 1/2)

Which gives:
1/2 * 12/13* 1/2 = 3/13 😃

Posted from my mobile device
User avatar
L
stne
Joined: 27 May 2012
Posts: 1724
Own Kudos [?]: 1575 [1]
Given Kudos: 643
Send PM
Re: One card is drawn at random from a pack of 52 cards. What is the proba [#permalink] One card is drawn at random from a pack of 52 cards. What is the proba   27 Dec 2021, 08:53
1
Kudos
KANNUPRIYA17
One card is drawn at random from a pack of 52 cards. What is the probability that the card drawn is NEITHER a 'spade' NOR a'10' NOR a'Red'.


A.9/52

B.3/13

C.10/13

D.21/26

E.43/52


There are in total \(52 \) cards.

\(13\) Spades ( Black )
\(13\) Clubs (Black )
\(13 \) Diamonds (Red)
\(13 \) Hearts (Red)

We DON'T NEED :
\(13\) Spades ( Black )
\(13 \) Diamonds (Red)
\(13 \) Hearts (Red)
\(10 \) of Hearts, \(10\) of Diamonds , \(10 \) of Spades and \(10 \) of Clubs.

However we have already removed \(10 \) of Spades, \(10\) of Diamonds , \(10 \) of Hearts above when we removed \(13\) of each kind.

Hence we have yet to remove ONLY \(10\) of Clubs.

Hence total removals = \(13 +13 +13 +1 = 40\)

Left with \(52 - 40 = 12 \)

Probability = \(\frac{12}{52} = \frac{3}{13}\)

Ans=B

Hope it's clear.
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 35126
Own Kudos [?]: 890 [0]
Given Kudos: 0
Send PM
Re: One card is drawn at random from a pack of 52 cards. What is the proba [#permalink] One card is drawn at random from a pack of 52 cards. What is the proba   07 May 2024, 21:14
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
GMAT Club Bot
gmatclubot
Re: One card is drawn at random from a pack of 52 cards. What is the proba [#permalink]
07 May 2024, 21:14
Moderator:
Bunuel
Math Expert
95944 posts