Final answer:
The probability of picking a card that is a letter in the word HEAD or a multiple of 3 is 0.35.
Step-by-step explanation:
In this problem, we need to determine the probability of picking a card that is either a letter in the word HEAD or a multiple of 3 from a bin containing 10 letter cards (A to J) and 10 numbered cards (1 to 10). To find the probability, we first determine the total number of favorable outcomes and the total number of possible outcomes.
The word HEAD has 4 letters (H, E, A, D) and there are 4 multiples of 3 (3, 6, 9, 10) in the given set of cards. However, card labeled 10 is not a multiple of 3, so it needs to be excluded. So, there are a total of 7 favorable outcomes.
The total number of cards in the bin is 20 (10 letters + 10 numbers). Therefore, the total number of possible outcomes is 20.
Now, we can determine the probability by dividing the number of favorable outcomes (7) by the number of possible outcomes (20).
P (card is a letter in the word HEAD or a multiple of 3) = 7/20 = 0.35