Question

you are dealt one card from a 52 - card deck. find the probability that you are not dealt a card with number from 4 to 6. click the icon to view a description of a standard deck of playing cards. the probability is (type an integer or a simplified fraction.)

Explanation:

Step1: Calculate the number of cards with number from 4 to 6

There are 4 suits (hearts, diamonds, clubs, spades) in a deck. For each number (4, 5, 6), there are 4 cards. So the number of cards with number from 4 to 6 is \(3\times4 = 12\) cards.

Step2: Calculate the number of non - (4 - 6) cards

The total number of cards in a deck is \(n = 52\). The number of non - (4 - 6) cards is \(52-12=40\) cards.

Step3: Calculate the probability

The probability formula is \(P(A)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). Here, the number of favorable outcomes (not getting 4 - 6) is 40 and the total number of outcomes is 52. So \(P=\frac{40}{52}=\frac{10}{13}\).

Answer:

\(\frac{10}{13}\)