Question
You are dealt one card from a 62 -card deck, Find the probability that you are not deall a card with number from 2 to 7 . The probability is \( \square \). (Type an integer or a simplified fraction.)
Ask by Mejia Ayala. in the United States
Mar 09,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The probability is \( \frac{19}{31} \).
Solution
1. The total number of cards in the deck is \(62\).
2. There are 6 numbers from 2 to 7. Assuming each number appears once per suit (usually 4 suits), the total number of cards with a number from 2 to 7 is
\[
6 \times 4 = 24.
\]
3. The number of cards that are not numbered 2 to 7 is
\[
62 - 24 = 38.
\]
4. Therefore, the probability of being dealt a card that is not numbered from 2 to 7 is
\[
\frac{38}{62}.
\]
5. Simplify the fraction by dividing the numerator and denominator by 2:
\[
\frac{38 \div 2}{62 \div 2} = \frac{19}{31}.
\]
The probability is \( \frac{19}{31} \).
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Simplify this solution Mind Expander
To find the probability of not being dealt a card numbered from 2 to 7 in a 62-card deck, let's first identify how many cards fall within that range. The numbers 2 to 7 include 2, 3, 4, 5, 6, and 7, which accounts for a total of 6 cards. With a 62-card deck, the total number of cards not numbered from 2 to 7 is \(62 - 6 = 56\). Now, the probability of being dealt a card not in that range is calculated by dividing the number of favorable outcomes (non-2 to 7 cards) by the total number of outcomes (total cards in the deck): \[ P(\text{not 2 to 7}) = \frac{56}{62} = \frac{28}{31} \] Thus, the probability is \(\frac{28}{31}\).
