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Sub 505 (Easy)|   Probability|            
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KarishmaB
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In a certain baord game, a stack of 48 cards, 8 of which 17 Jul 2017, 09:11
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longhaul123
there are total of 48 cards out of which 8 are stock cards so the probability of picking a card from the stock card is 8/48 =S and the other cards are 40/48=N therefore, NNS=5/6*4/5*1/6=1/9 where am i going wrong??
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The probability of picking a Non-stock card, Non-stock card and a Stock card is different from this question.

Here, you are given that the first two are non-stock cards so you do not need to account for the probability of those being non-stock. It is already known that they are.

Also, the probability of selecting NNS would be (40/48)*(39/47)*(8/46)
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In a certain baord game, a stack of 48 cards, 8 of which 02 Aug 2020, 07:15
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In a certain board game, a stack of 48 cards, 8 of which represent shares of stock, are shuffled and then placed face down. If the first 2 cards selected do not represent shares of stock, what is the probability that the third card selected will represent a share of stock?

A. 1/8
B. 1/6
C. 1/5
D. 3/23
E. 4/23
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GIVEN: Among the 48 cards, 8 cards represent shares of stock.

The first 2 cards selected do NOT represent shares of stock, which means there are 46 cards REMAINING, and 8 of those remaining cards represent shares of stock.

P(the third card selected represents a share of stock) = 8/46 = 4/23

Answer: E

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In a certain baord game, a stack of 48 cards, 8 of which 23 Apr 2026, 21:35
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hi KarishmaB
I understand your approach, i have a doubt. The probability of picking the stack card shouldn't be same in any draws? that's why i picked 1/8. Or is that approach applicable only in the replacement questions?
I have seen questions asking what is the probability of getting a head in 100th toss when 150 coins are tossed. The probability will always be 1/2, no matter what the draw is. Am i making sense?

Please respond.

Thanks in advance,
Swetha
KarishmaB


Yes you can. You already know that the first 2 cards are not stock cards. It's like we placed them face up. They anyway are out of the picture. Now we have 46 cards and 8 of them are stock cards. So the probability that the card we pick is a stock card is 8/46 = 4/23.

The probability of picking a stock card keeps increasing as we keep pulling out the non stock cards.
Think: You have 5 cards and 1 of them is the Queen. What is the probability that you will pull out a queen? It's 1/5. What happens after you pull out a non queen? The probability of pulling out a queen now becomes 1/4. It keeps increasing till you reach the last card. If you still haven't pulled out a queen, the last one must be the queen and the probability becomes 1.

Another thing to think about: What happens if you don't know what the first two cards are i.e. what is the probability of picking a share card on the third pick (you don't know what the first two picks are).
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In a certain baord game, a stack of 48 cards, 8 of which 23 Apr 2026, 21:50
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SwethaReddyL
hi KarishmaB
I understand your approach, i have a doubt. The probability of picking the stack card shouldn't be same in any draws? that's why i picked 1/8. Or is that approach applicable only in the replacement questions?
I have seen questions asking what is the probability of getting a head in 100th toss when 150 coins are tossed. The probability will always be 1/2, no matter what the draw is. Am i making sense?

Please respond.

Thanks in advance,
Swetha

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No. The key difference is this: in the coin example, each toss is independent, so the 100th toss still has probability 1/2 for heads. Here, the cards are drawn without replacement, so the probabilities can change from draw to draw depending on what has already been removed.

In this question, we are told that the first 2 cards are not stock cards. That means 2 non-stock cards are gone, so 46 cards remain, and the number of stock cards is still 8. Therefore, the probability that the third card is a stock card is 8/46 = 4/23, not 1/8.
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In a certain baord game, a stack of 48 cards, 8 of which 23 Apr 2026, 23:20
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... and 1/8 would be the answer if you were putting the card back in the pile and shuffling.

SwethaReddyL
hi KarishmaB
I understand your approach, i have a doubt. The probability of picking the stack card shouldn't be same in any draws? that's why i picked 1/8. Or is that approach applicable only in the replacement questions?
I have seen questions asking what is the probability of getting a head in 100th toss when 150 coins are tossed. The probability will always be 1/2, no matter what the draw is. Am i making sense?

Please respond.

Thanks in advance,
Swetha

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