A deck of cards contains red cards numbered \( 1,2,3 \), blue cards numbered \( 1,2,3,4,5 \) and green cards numbered \( 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21 \). If a single card is picked at random, what is the probability that the card is blue? - Give your answer as a fraction.

To find the probability that a randomly picked card is blue, we first need to determine the total number of cards in the deck and the number of blue cards. 1. **Count the red cards**: There are 3 red cards numbered \(1, 2, 3\). 2. **Count the blue cards**: There are 5 blue cards numbered \(1, 2, 3, 4, 5\). 3. **Count the green cards**: There are 21 green cards numbered \(1, 2, 3, \ldots, 21\). Now, we can calculate the total number of cards in the deck: \[ \text{Total cards} = \text{Red cards} + \text{Blue cards} + \text{Green cards} = 3 + 5 + 21 = 29 \] Next, we find the number of blue cards, which is 5. Now, we can calculate the probability \(P\) that a randomly picked card is blue: \[ P(\text{blue}) = \frac{\text{Number of blue cards}}{\text{Total number of cards}} = \frac{5}{29} \] Thus, the probability that the card is blue is \[ \boxed{\frac{5}{29}}. \]