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dalvyx [7]
3 years ago
6

1) Given P(A) = 0.3 and P(B) = 0.5, do the following.

Mathematics
1 answer:
Delicious77 [7]3 years ago
6 0

Answer:

1) a) 0.8

b) 0.6

2) a) 0.08

b) 0.14

Step-by-step explanation:

1) Given

P(A) = 0.3 and P(B) = 0.5

Let us learn about a formula:

P(A\ or\ B) = P(A) +P(B) -P(A\ and\ B)\\OR\\P(A\cup B) = P(A) +P(B) -P(A\cap B)

(a) If A and B are mutually exclusive i.e. no common thing in the two events.

In other words:

P(A\ and\ B) = P(A \cap B) = 0

Using above formula:

P(A\ or\ B) = P(A) +P(B) -P(A\ and\ B)\\\Rightarrow P(A\ or\ B) = 0.3 + 0.5 -0 = \bold{0.8}

(b)  P(A and B) = 0.2

Using above formula:

P(A\ or\ B) = P(A) +P(B) -P(A\ and\ B)\\\Rightarrow P(A\ or\ B) = 0.3 + 0.5 -0.2 = \bold{0.6}

*************************************

1) Given

P(A) = 0.4 and P(B) = 0.2

Let us learn about a formula:

P(A\ and\ B) = P(B) \times P(A/B)  for dependent events

P(A\ and\ B) = P(A) \times P(B) for independent events.

(a) If A and B are independent events :

Using the above formula for independent events:

P(A\ and\ B) = 0.4 \times 0.2 = \bold{0.08}

(b)  P(A / B) = 0.7

Using above formula:

P(A\ and\ B) = P(B) \times P(A/B) = 0.2 \times 0.7 = \bold{0.14}

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3 years ago
Omar works as a tutor for $15 an hour and as a waiter for $7 an hour. This month, he worked a combined total of 83 hours at his
Alborosie

Answer: 8t+581

Step-by-step explanation:

<h3> The complete exercise is: "Omar works as a tutor for $15 an hour and as a waiter for $7 an hour. This month, he worked a combined total of 83 hours at his two jobs. Let "t" be the number of hours Omar worked as a tutor this month. Write an expression for the combined total dollar amount he earned this month."</h3><h3 />

Let be "t" the number of hours Omar worked as a tutor this month and "w" the number of hours Omar worked as a waiter this month.

Based on the data given in the exercise, you know that Omar worked a combined total of 83 hours this month.

Then, you can represent the number of hours he worked as a waiter this month with this equation:

w=83-t

Since he earns  $15 per hour working has a tutor and $7 per hour working as a waiter, you can write the following expresion to represent the total money earned:

15t+7w

Since w=83-t, you can substitute it into the expression and then simplify it in order to find the final expression that represents the total amount of money Omar earned this month.

This is:

15t+7(83-t)=15t+581-7t=8t+581

4 0
3 years ago
What is the midpoint of the line segment with endpoints ( 3.5,2.2) and (1.5,-4.8)?
Fantom [35]

Answer:

Option A) (2.5,-1.3) is correct

The midpoint of the given line segment is M=(2.5,-1.3)

Step-by-step explanation:

Given that the line segment with end points (3.5, 2.2) and (1.5, -4.8)

To find the mid point of these endpoints midpoint formula is M=\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)

Let (x_1,y_1) be the point (3.5, 2.2) and (x_2, y_2) be the point (1.5, -4.8)

substituting the points in the formula

M=\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)

M=\left(\frac{3.5+1.5}{2}, \frac{2.2-4.8}{2}\right)

=\left(\frac{5}{2}, \frac{-2.6}{2}\right)

=\left(2.5,-1.3\right)

Therefore M=(2.5,-1.3)

The midpoint of the given line segment is M=(2.5,-1.3)

8 0
3 years ago
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