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3 years ago

14

Sarah has two tests at school next week, a math test and a physics test. Let A represent the event that she passes her math test

and B represent the event that she passes her physics test. If A and B are independent events with P(A)=0.30 and P(A AND B)=0.21, find P(B)

1 answer:

koban [17]3 years ago

3 0

Answer:

P(B)=0.7

Step-by-step explanation:

When the events do not affect each other, they are known as independent events. In other words, two events are independent if the outcome of the second event is not affected by the outcome of the first event.

If A and B are independent events, the probability that both events will occur is the product of the probabilities that the individual events will occur:

P(A and B)= P(A)*P(B)

In this case, P(A and B)= 0.21 and P(A)= 0.30

Replacing:

0.21=0.30*P(B)

Solving:

$\frac{0.21}{0.30} =P(B)$

<u><em>0.7=P(B)</em></u>

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tankabanditka [31]

Answer:

$(a)\ AB = \frac{7}{\sin (B)}$ $\to Yes$

$(b)\ AB = \frac{24}{\cos (B)}$ $\to Yes$

$(c)\ AB = \frac{24}{\cos (A)}$ $\to No$

$(d)\ AB = \frac{7}{\cos (A)}$ $\to Yes$

Step-by-step explanation:

Given

$BC =24$

$AC = 7$

Required

Select Yes or No for the given options

$(a)\ AB = \frac{7}{\sin (B)}$ $\to Yes$

Considering the sine of angle B, we have:

$\sin(B) = \frac{Opposite}{Hypotenuse}$

$\sin(B) = \frac{7}{AB}$

Make AB, the subject

$AB = \frac{7}{\sin(B)}$

$(b)\ AB = \frac{24}{\cos (B)}$ $\to Yes$

Considering the cosine of angle B, we have:

$\cos(B) = \frac{Adjacent}{Hypotenuse}$

$\cos(B) = \frac{24}{AB}$

Make AB the subject

$AB = \frac{24}{\cos(B)}$

$(c)\ AB = \frac{24}{\cos (A)}$ $\to No$

Considering the cosine of angle B, we have:

$\cos(A) = \frac{Adjacent}{Hypotenuse}$

$\cos(A) = \frac{7}{AB}$

Make AB the subject

$AB = \frac{7}{\cos(A)}$

$(d)\ AB = \frac{7}{\cos (A)}$ $\to Yes$

<em>This has been shown in (c) above</em>

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3 years ago