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riadik2000 [5.3K]
3 years ago
8

Roger will flip a coin 3 times. Which 2 events are disjoint?

Mathematics
1 answer:
Ganezh [65]3 years ago
7 0

Answer: D. Getting at least 2 heads and Getting at least 2 tails

=========================================================

Explanation:

Choice A is not disjoint because "getting at least 1 tail" could have the sequence TTH. We see that we have two tails and exactly one head. So the events "getting exactly 1 head" and "Getting at least 1 tail" are possible to occur at the same time; therefore, they aren't disjoint events. Disjoint events are two events that cannot occur simultaneously. An example would be flipping heads and tails on the same coin at the same time.

Choice B is also not disjoint. We could have the sequence THT, which has at least one head and at least one tail. "At least" means that amount or more.

Choice C is also not disjoint. We could have the sequence HTT. This has exactly one head and at least two tails.

Choice D is the only thing left. It must be the answer. It is not possible to get 2 heads and 2 tails when Roger only flips the coin 3 times. He would need to flip the coin at least 4 times for this to happen. The portions "at least" don't even need to be considered. So this shows how choice D is disjoint.

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<u>Step-by-step explanation:</u>

Here we have , cosxtanx - 2 cos^2 x=-1. Let's solve :

⇒  cosxtanx - 2 cos^2 x=-1

⇒  cosx(\frac{sinx}{cosx}) - 2 cos^2 x=-1

⇒  sinx = 2 cos^2 x-1

⇒  sinx = 2 (1-sin^2x)-1

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By quadratic formula :

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⇒ sinx = \frac{-1 \pm3}{4}

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Therefore , Solution to equationcosxtanx - 2 cos^2 x=-1 for all real values of x is  x=2k\pi + \frac{\pi}{6}  , x=2k\pi + \frac{5\pi}{6} .

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Let's solve this question by step by step.

Layout equation.

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Step 2: Flip the equation.

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Step 4: Divide both sides by -8.

-8k/-8=-40/-8

The answer for this problem is k=5.

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