Find the probability of drawing a spade on each of two consecutive dra...
in a pack of card there are total 52 Cards
Spade cards are 13
Probability that two consecutive cards drawn from a well shuffled pack of cards are spade = ¹³C₂ / ⁵²C₂
= 13 * 12 / 52 * 51
= 12 / 4 * 51
= 3/51
= 1/17
other ways
probability of Choosing 1st card as spade = (13/52) = 1/4
Probability of choosing 2nd spade card = 12/51 = 4/17
(1/4)(4/17) = 1/17
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Find the probability of drawing a spade on each of two consecutive dra...
To find the probability of drawing a spade on each of two consecutive draws from a well-shuffled pack of cards without replacement, we can break down the problem into two steps:
Step 1: Probability of drawing a spade on the first draw
Step 2: Probability of drawing a spade on the second draw, given that a spade was drawn on the first draw
Step 1: Probability of drawing a spade on the first draw
In a well-shuffled pack of cards, there are 52 cards in total. Out of these 52 cards, there are 13 spades. Therefore, the probability of drawing a spade on the first draw is given by:
Probability of drawing a spade on the first draw = Number of favorable outcomes / Total number of outcomes
Probability of drawing a spade on the first draw = 13 / 52
Probability of drawing a spade on the first draw = 1 / 4
Step 2: Probability of drawing a spade on the second draw, given that a spade was drawn on the first draw
After the first draw, there are now 51 cards left in the pack, and 12 spades remaining. Therefore, the probability of drawing a spade on the second draw, given that a spade was drawn on the first draw, is given by:
Probability of drawing a spade on the second draw = Number of favorable outcomes / Total number of outcomes
Probability of drawing a spade on the second draw = 12 / 51
Now, we need to find the probability of both events happening together (drawing a spade on the first draw and drawing a spade on the second draw). Since these events are independent, we can multiply their probabilities:
Probability of drawing a spade on both draws = Probability of drawing a spade on the first draw * Probability of drawing a spade on the second draw
Probability of drawing a spade on both draws = (1 / 4) * (12 / 51)
Simplifying this expression, we get:
Probability of drawing a spade on both draws = 12 / (4 * 51)
Probability of drawing a spade on both draws = 12 / 204
Probability of drawing a spade on both draws = 1 / 17
Therefore, the correct answer is option 'B' (1/221).
Note: It is important to remember that when drawing without replacement, the total number of outcomes changes for each subsequent draw as the number of cards in the pack decreases.
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