A nontraditional deck of cards has 30 total cards: 5 hearts, 10 clubs, 8 spades, and 7 diamonds. The cards are shuffled, and the top card is noted. This process is repeated 100 times. What is the probability the top card is spades in more than 30% of the sample?Find the z-table here.

The probability of drawing a spade on one trial is 8/30 ≈ 0.267. For 100 trials, the sample proportion has standard deviation √[0.267(1 − 0.267)/100] ≈ 0.044. The z-score for a sample proportion of 0.30 is (0.30 − 0.267)/0.044 ≈ 0.75; the area above this z-score is about 0.224. Therefore, the probability is 0.224, choice A.

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