Question - Finding Probability of Picking Even Numbers from a Set of Cards
Solution:
This problem is about finding the probability of picking an even number from a set of cards labeled with numbers from 1 to 7, and then, without replacing the first card, picking another even number.Let's determine the probability step by step.1. The probability of picking an even number (2, 4, 6) on the first draw:There are 3 even numbers out of 7 total numbers, so the probability is $$ \frac{3}{7} $$.2. The probability of picking another even number on the second draw:After one even card is removed, there are now 2 even numbers remaining, and only 6 cards in total to choose from. So the probability for the second draw is $$ \frac{2}{6} $$ which simplifies to $$ \frac{1}{3} $$.Now we multiply the probabilities of both events happening in sequence, which are independent in this context:$$ \frac{3}{7} \times \frac{1}{3} = \frac{3}{21} $$, which simplifies to $$ \frac{1}{7} $$.So, the probability of drawing an even number and then another even number without replacement is $$ \frac{1}{7} $$.
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