Final answer:
The sample space for the deck of cards has 7 elements. The probability of drawing a yellow card (P(A)) is approximately 0.57, and the probability of drawing an even-numbered card (P(B)) is approximately 0.43.
Step-by-step explanation:
A student is asking about probabilities relating to a special deck of cards with purple and yellow cards, each with numbered values. The student wishes to know the number of elements in the sample space, the probability of drawing a yellow card (P(A)), and the probability of drawing an even-numbered card (P(B)).
a) The sample space consists of all possible outcomes when drawing one card from the deck. There are 3 purple cards numbered 1, 2, and 3, and 4 yellow cards numbered 1, 2, 3, and 4. Thus, the sample space has 3 (purple cards) + 4 (yellow cards) = 7 elements.
- Purple 1 (P1)
- Purple 2 (P2)
- Purple 3 (P3)
- Yellow 1 (Y1)
- Yellow 2 (Y2)
- Yellow 3 (Y3)
- Yellow 4 (Y4)
b) The probability of drawing a yellow card, P(A), is the number of yellow cards divided by the total number of cards: P(A) = 4 yellow cards/7 total cards ≈ 0.57 (to two decimal places).
c) The probability of drawing an even-numbered card, P(B), is the number of even-numbered cards divided by the total number of cards. There are two even-numbered yellow cards (2 and 4) and one even-numbered purple card (2), making a total of 3. Therefore, P(B) = 3 even-numbered cards/7 total cards ≈ 0.43 (to two decimal places).