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A deck of cards contains RED cards numbered \( 1,2,3 \) and BLUE cards numbered 1,2 . Let \( R \) be the event of drawing a red card, \( B \) the event of drawing a blue card, \( E \) the event of drawing an even numbered card, and \( O \) the event of drawing an odd card. Drawing the Red 3 is an example of which of the following events? Select all correct answers. Select all that apply: \( \square O^{\prime} \) \( \square B \) OR \( E \) \( \square B \) OR \( O \) \( \square B^{\prime} \) \( \square B \) AND \( E \) \( \square E^{\prime} \) \( \square \)

Ask by Donnelly Sullivan. in the United States
Feb 27,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

Drawing the Red 3 is an example of the following events: - B OR O - B′ - E′

Solution

We have a deck with RED cards numbered 1, 2, 3 and BLUE cards numbered 1, 2. The card being drawn is Red 3. Let’s go through each event: 1. O′ (the complement of odd) means “not odd,” i.e. even. Since 3 is odd, Red 3 is not in O′. 2. B OR E means “blue card or even-numbered card.” Red 3 is a red card (not blue) and 3 is odd (not even), so it does not belong to this event. 3. B OR O means “blue card or odd-numbered card.” Although Red 3 is not blue, it is odd, so it qualifies for this event. 4. B′ means “not blue”. Red 3 is red and thus is in B′. 5. B AND E means “blue card and even-numbered card.” Red 3 fails both: it is not blue and 3 is odd, so it does not belong. 6. E′ means “not even” (i.e. odd). Since 3 is odd, Red 3 is in E′. Thus, the events that include drawing the Red 3 are:  • B OR O  • B′  • E′

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Sure! Let's break down the event of drawing the Red 3: 1. **Red 3** is an odd number (so it belongs to the event \( O \)), which means it does not belong to the even numbered cards (event \( E \)). Therefore, it is NOT part of event \( E \) and is indeed part of \( O \). 2. Since Red 3 is red, it cannot be a blue card (event \( B \)). So we can exclude options involving \( B \) directly. Now, let's evaluate the options: - \( O^{\prime} \): This is NOT correct as Red 3 is odd (part of event \( O \)). - \( B \) OR \( E \): This is NOT correct since Red 3 is not blue and is not even. - \( B \) OR \( O \): This is correct as Red 3 is odd. - \( B^{\prime} \): This is correct since Red 3 is red (not blue). - \( B \) AND \( E \): This is NOT correct because Red 3 is neither blue nor even. - \( E^{\prime} \): This is correct since Red 3 is odd and is hence not even. So the correct answers to select would be: - \( B \) OR \( O \) - \( B^{\prime} \) - \( E^{\prime} \)

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