Using a standard deck of 52 cards, Lisa drew a card, recorded the suit of the card picked, then replaced it back in the deck. She continued this for a total of 40 draws. The table shows the frequency of each type of card drawn.

Diamonds Spades Hearts Clubs
7 11 9 13

Determine the experimental probability of not selecting a diamond.
P(not diamond) = 82.5%
P(not diamond) = 72.5%
P(not diamond) = 10%
P(not diamond) = 7%

1 answer

To determine the experimental probability of not selecting a diamond, we first need to calculate the total number of draws and the number of draws that were not diamonds.

  1. Total number of draws: 40 (as stated in the problem).
  2. Number of diamonds drawn: 7 (as stated in the frequency table).

Now, we can calculate the number of draws that were not diamonds:

\[ \text{Number of not diamonds} = \text{Total draws} - \text{Number of diamonds drawn} = 40 - 7 = 33 \]

Next, we calculate the experimental probability of not selecting a diamond:

\[ P(\text{not diamond}) = \frac{\text{Number of not diamonds}}{\text{Total draws}} = \frac{33}{40} \]

To convert this fraction into a percentage:

\[ P(\text{not diamond}) = \frac{33}{40} \times 100 \]

Calculating this gives:

\[ P(\text{not diamond}) = 0.825 \times 100 = 82.5% \]

Thus, the experimental probability of not selecting a diamond is:

\[ P(\text{not diamond}) = 82.5% \]

The correct answer is P(not diamond) = 82.5%.