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 find the total number of draws and the number of draws that resulted in diamonds.

From the table, the frequencies of the suits are:

  • Diamonds: 7
  • Spades: 11
  • Hearts: 9
  • Clubs: 13

The total number of draws is: \[ 7 + 11 + 9 + 13 = 40 \]

Next, we find the number of draws that were not diamonds: \[ \text{Total draws} - \text{Number of diamonds} = 40 - 7 = 33 \]

Now we can calculate the experimental probability of not selecting a diamond: \[ P(\text{not diamond}) = \frac{\text{Number of draws not diamonds}}{\text{Total draws}} = \frac{33}{40} \]

To express this as a percentage: \[ P(\text{not diamond}) = \frac{33}{40} \times 100 = 82.5% \]

Therefore, the experimental probability of not selecting a diamond is: \[ \boxed{82.5%} \]