Question

one card is randomly selected from a deck of cards. find the odds in favor of drawing a red card. click the icon to view a description of a standard deck of playing cards. the odds are (simplify your answer.)

Explanation:

Step1: Determine the number of red cards and non - red cards

A standard deck has 52 cards. There are 26 red cards (13 hearts and 13 diamonds) and \(52 - 26=26\) non - red cards (13 spades and 13 clubs).

Step2: Calculate the odds in favor

The formula for odds in favor of an event \(E\) is \(\text{Odds in favor}=\frac{\text{Number of favorable outcomes}}{\text{Number of unfavorable outcomes}}\).
For drawing a red card, the number of favorable outcomes (red cards) is \(n(R)=26\), and the number of unfavorable outcomes (non - red cards) is \(n(\text{non}-R)=26\).
So, the odds in favor of drawing a red card is \(\frac{26}{26}\)

Answer:

\(1:1\)