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 of picking a blue card, we first need to determine the total number of cards in the deck. - The red cards are 3 in total: 1, 2, 3. - The blue cards are 5 in total: 1, 2, 3, 4, 5. - The green cards are 21 in total: 1, 2, 3, ..., 21. Adding these together, the total number of cards is: \[ 3 + 5 + 21 = 29 \] Now, the number of favorable outcomes (picking a blue card) is 5 (the blue cards). Therefore, the probability \( P \) of picking a blue card is calculated as follows: \[ P(\text{Blue}) = \frac{\text{Number of blue cards}}{\text{Total number of cards}} = \frac{5}{29} \] The probability that the card is blue is \(\frac{5}{29}\).