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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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