Question

Data analysis Given a standard deck of cards, To find the probability of drawing three red cards one by one by not replacing any of the card.

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asked 2021-05-28
Data analysis
Given a standard deck of cards,
To find the probability of drawing three red cards one by one by not replacing any of the card.

Answers (1)

2021-05-29
At First card draw,
total cards in deck \(= 52\)
Total red cards \(= 26\)
Probability that first drawn card is red \(= 26/52\)
At second card draw,
total cards in deck \(= 51\)
Total red cards \(= 25\)
Probability that first drawn card is red \(= 25/51\)
At third card draw,
total cards in deck \(= 50\)
Total red cards \(= 24\)
Probability that first drawn card is red \(= 24/50\)
Hence final probability that three drawn cards one after one with replacing are red
\((26/52)\times(25/51)\times(24/50)\)
\(=(1/2)\times(25/51)\times(12/25)\)
\(=(1\times25\times12)/(2\times51\times25)\)
\(=300/2550\)
\(=0.1176\) (rounded to 4 decimals)
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