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Chapter 11: Problem 5

You are dealt one card from a 52-card deck. Find the probability that you are not dealt a picture card.

Short Answer

Expert verified
The probability of not drawing a picture card from a standard deck on a single draw is \( \frac{77}{100} \) or 77%

Step by step solution

01

Identify total outcomes

A standard deck contains 52 cards. Therefore, there are 52 possible outcomes when you pick one card.
02

Identify desired outcomes

Picture cards are Kings, Queens, or Jacks. Each suit (hearts, diamonds, clubs, spades) has 1 King, 1 Queen, and 1 Jack. So, there are 4 Kings, 4 Queens, and 4 Jacks in a deck, giving a total of 12 picture cards.
03

Calculate Probability of Getting a Picture Card

The probability of an event happening is calculated by dividing the number of ways that event can happen by the total number of outcomes. In this case, that's the number of picture cards (12) divided by the total number of cards (52). So, the probability of drawing a picture card is \( \frac{12}{52} = \frac{23}{100} \). This means that, if you picked a card at random from a full deck, you'd have about a 23% chance of getting a picture card.
04

Calculate the Probability of Not Getting a Picture Card

The probability of an event not happening is 1 minus the probability the event will happen. So, the probability not getting a picture card is \( 1 - \frac{23}{100} = \frac{77}{100} \). This means that, if you picked a card at random from a full deck, you'd have about a 77% chance of not getting a picture card.

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