4. Determine whether the events are mutually exclusive. Then d...

Question

4. Determine whether the events are mutually exclusive. Then determine whether the events are independent or dependent. Explain your reasoning.

Event A: A bowler having the highest game in a 40-game tournament

Event B: Losing the bowling tournament

Accepted Answer

Hello there. Today we're gonna solve the following practice problem together. So, first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. A student participates in a spelling bee. Consider these events. Event G, the student spells the most words correctly in a single round. Event H, the student is eliminated before the final round. Are these events mutually exclusive? Are they independent or dependent? Awesome. So apparently, for this particular prompt. We're asked to investigate event G and event H, and we're asked to determine whether or not these events are mutually exclusive, and we're asked to determine if they are independent or dependent. So we're ultimately trying to solve for two separate answers. So with that in mind, Our first step is we need to check if the events are mutually exclusive. So focusing our attention on event G first, which I'll just call G for short. So event G is spelling the most words correctly in a round. And event H, which I'll call H for short, is being eliminated before the final round. So, as we should note and recall, It is possible for a student to spell the most words correctly in one round as an event G, but still be eliminated before the final round event H. So with that in mind, therefore, without a doubt, both events can happen together, so they are not mutually exclusive. So they are not, I'll put a red X, they are not mutually exclusive. So they are not mutually exclusive, which you'll call ME for short. So they're not, once again, not mutually exclusive. Our second step Yes we need to check if the events are independent or dependent. So, as you should recall a note, if a student spells the most words correctly in a round such as event G, it likely increases their chance of advancing and therefore, as a result, reduces the chance of being eliminated before the final round as stated in event H. So therefore, without a doubt, knowing that event G occur how event G occurs will affect the likelihood of event H from occurring. So that will mean that it will make the events dependent, so the events will be dependent. So that means our final set of answers without a doubt have to be once again. Not mutually exclusive and dependent, and that's it. We've officially solved for this particular problem. Thank you so much for watching. Hopefully that helped, and I can't wait to see you in the next video. Bye.

4. Determine whether the events are mutually exclusive. Then determine whether the events are independent or dependent. Explain your reasoning.
Event A: A bowler having the highest game in a 40-game tournament
Event B: Losing the bowling tournament

Key Concepts

Mutually Exclusive Events

Independent Events

Dependent Events

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