To find the probability that neither Sammy nor Hannah draws leeks from the available cards, we need to carefully calculate the probabilities of two events happening:
1. Sammy does not draw leeks.
2. Given that Sammy did not draw leeks, Hannah does not draw leeks either.
First, let's identify the total number of cards available and what happens after each draw:
- Total number of cards: 6
- Only one card has leeks, so there are 5 cards without leeks.
### Step-by-Step Calculation:
Step 1: Probability that Sammy does not draw leeks
- Number of non-leek cards: 5
- Number of total cards: 6
So, the probability that Sammy does not draw the card with leeks is:
[tex]\[ P(\text{Sammy does not draw leeks}) = \frac{5}{6} = 0.8333333333333334 \][/tex]
Step 2: Probability that Hannah does not draw leeks, given that Sammy did not draw leeks
- After Sammy draws a card (which is not leeks), there are 5 cards left.
- Out of these 5 remaining cards, 4 do not contain leeks (since one non-leek card was drawn by Sammy).
Thus, the probability that Hannah does not draw the card with leeks, given that Sammy did not draw leeks, is:
[tex]\[ P(\text{Hannah does not draw leeks} \mid \text{Sammy did not draw leeks}) = \frac{4}{5} = 0.8 \][/tex]
Step 3: Probability that neither Sammy nor Hannah draws leeks
To find the combined probability that neither Sammy nor Hannah draws the leeks card, we multiply the individual probabilities:
[tex]\[ P(\text{Neither draw leeks}) = P(\text{Sammy does not draw leeks}) \times P(\text{Hannah does not draw leeks} \mid \text{Sammy did not draw leeks}) \][/tex]
[tex]\[ P(\text{Neither draw leeks}) = 0.8333333333333334 \times 0.8 = 0.6666666666666667 \][/tex]
Step 4: Rounding the final probability
Finally, we round this probability to two decimal places:
[tex]\[ \text{Rounded probability} = 0.67 \][/tex]
Thus, the probability that neither Sammy nor Hannah draws leeks is:
[tex]\[ \boxed{0.67} \][/tex]
