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3 years ago

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Which of the following pairs of events are mutually exclusive? Rolling a die; A={Rolling an even number}, B={Rolling a number gr

eater than 4} Picking a card; A= {Selecting a 7}, B={Selecting a Heart} Tossing a coin twice; A ={no Heads}, B={at least 1 Head} Rolling two 6-sided dice; A={rolling a sum of 4}, B={rolling a 3 on one die}

1 answer:

choli [55]3 years ago

6 0

Answer:

Tossing a coin twice; A ={no Heads}, B={at least 1 Head}

Step-by-step explanation:

Mutually exclusive:

If two events are mutually exclusive, if one events happen, the other cannot happen, and vice-versa.

Rolling a die; A={Rolling an even number}, B={Rolling a number greater than 4}

A die has the following outcomes: 1,2,3,4,5,6

Even numbers: 2,4,6

Greater than 4: 5, 6

6 is an outcome of both events A and B, so they are not mutually exclusive.

Picking a card; A= {Selecting a 7}, B={Selecting a Heart}

Cards numbered from 1 to 13, each number with 4 types. So we can have a card of hearts numbered 7, which means that these events are not mutually exclusive.

Tossing a coin twice; A ={no Heads}, B={at least 1 Head}

If you get no heads, the probability of at least 1 head is 0.

If you get at least 1 head, the probability of no heads is 0.

This means that this is the answer, that is, these events are mutually exclusive.

Rolling two 6-sided dice; A={rolling a sum of 4}, B={rolling a 3 on one die}

(3,1) or (1,3) has a sum of 4 and a 3 on one die, which means that these events are not mutually exclusive.

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Step-by-step explanation:

We are going to see if the exponential curve is of the form:

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If you are given the $y-$ intercept, then $a$ is easy to find.

It is just the $y-$ coordinate of the $y-$ intercept is your value for $a$ .

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So $a=8$ .

So our function so far looks like this:

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Now to find $b$ we need another point. We have two more points. So we will find $b$ using one of them and verify for our resulting equation works for the other.

Let's do this.

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So when $x=1$ , $y=10$ .

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Let's try it. So the last point given that we need to satisfy is $(2,12.5)$ .

This says when $x=2$ , $y=12.5$ .

Let's replace $x$ with 2 and see what we get for $y$ :

$y=8 \cdot (\frac{5}{4})^2$

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