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3 years ago

If P(A) = 0.3 and P(B) = 0.6 what is P(A or B) if the two events are independent?

Mathematics

1 answer:

Katena32 [7]3 years ago

6 0

Answer:

P(A or B) is 0.72

Step-by-step explanation:

Given : P(A) = 0.3 and P(B) = 0.6

To Find:P(A or B) = P(A∪B)

Solution :

We are given that A and B are two independent events

Property : If A and B are independent events then $P(A \cap B) = P(A) \times P(B)$

So, $P(A \cap B) = P(A) \times P(B)$

$P(A \cap B) =0.3 \times 0.6$

$P(A \cap B) =0.18$

Formula : $P(A \cup B)=P(A)+P(B)-P(A \cap B)$

$P(A \cup B)=0.3+0.6-0.18$

$P(A \cup B)=0.72$

Hence P(A or B) is 0.72

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a collection of dimes and quarters is worth $19.85. There are 128 coins in all. How many of each type of coin are in the collect

PolarNik [594]

Number of dimes were 81 and number of quarters were 47

Solution:

Let "d" be the number of dimes

Let "q" be the number of quarters

We know that,

value of 1 dime = $ 0.10

value of 1 quarter = $ 0.25

Given that There are 128 coins in all

number of dimes + number of quarters = 128

d + q = 128 ------ eqn 1

Also given that collection of dimes and quarters is worth $19.85

number of dimes x value of 1 dime + number of quarters x value of 1 quarter = 19.85

$d \times 0.10 + q \times 0.25 = 19.85$

0.1d + 0.25q = 19.85 -------- eqn 2

Let us solve eqn 1 and eqn 2

From eqn 1,

d = 128 - q -------- eqn 3

Substitute eqn 3 in eqn 2

0.1(128 - q) + 0.25q = 19.85

12.8 - 0.1q + 0.25q = 19.85

12.8 + 0.15q = 19.85

0.15q = 7.05

Therefore from eqn 3,

d = 128 - q

d = 128 - 47

Thus number of dimes were 81 and number of quarters were 47

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3 years ago

Help me pls... ....

musickatia [10]

Step-by-step explanation:

1 yard = 3 feet

1 foot = 12 inches

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100 yards = 100×3×12 inches = 3600 inches

again, 1 yard = 3 feet

8 ft = 8/3 = 2.67 yards = 2 2/3 yards

1 gallon = 8 pints

1 liter = 1000 milliliters (remember, "mili" means 1/1000).

therefore,

2.2 liters = 2.2×1000 = 2200 milliliters

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1 milliliter = 1/1000 liter

670 milliliters = 670 × 1/1000 liter = 670/1000 liter =

= 0.67 liter

1 kg (kilogram) = 1000 grams ("kilo" means 1000).

we have 3 layers.

each layer weighs (cake plus icing)

1/2 kg + 100 g = 500 g + 100 g = 600 g

3 layers then weigh

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the additional candle weighs 250 g.

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1800 g + 250 g = 2050 g = 2.05 kg

area is 110 m².

1 m = 100 cm ("centi" means 1/100).

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110 × 10000 = 1,100,000 cm²

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2 years ago

The volume, V, of a sphere in terms of its radius, r, is given by , V(r)=4/3(pie)r^3. Express r as a function of V, and find the

kipiarov [429]

Answer:

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2 years ago

Read 2 more answers

What is the solution to the system? 1. x-y + 2 z = -7 2. y + z =1 3. x-2 y - 3 z = 0

kvv77 [185]

You'd find this problem easier to understand and do if you'd please list the defining equations vertically and line up variables:

1. x - 1y + 2 z = -7

2. y + 1z = 1

3. x - 2 y - 3 z = 0 Now eliminate the line numbers:

x - 1y + 2 z = -7

1y + 1 z = 1

x - 2 y - 3 z = 0

Let's use the elimination method to eliminate variable z: Seeing that z = 1 - y, we transform the first equation into 1x - 1y + 2(1-y) = -7

and the third into x - 2y - 3(1-y) = 0.

Simplifying 1x - 1y + 2(1-y) = -7

and x - 2y - 3(1-y) = 0,

we get

1x - 2y - 3 + 3y) = 0 and 1x - 1y + 2 - 2y = -7

which in turn simplify to

1x + y = 3 and 1x - 3y = -9

Having eliminated the variable z, we now focus on eliminating x. Mult. the 1st equation by -1, obtaining -1x - 1y = -3. Add this result to 1x - 3y = -9:

0 - 4y = -12, which tells us that y = 3. Subbing 3 for y in 1x + 1y = 3 tells us that x = 0.

All we have left to determine is the vaue of z.

Borrowing Equation 3, from above, we get x - 2 y - 3 z = 0, and into this equation we substitute x = 0 and y = 3: 0 -2(3) - 3z = 0.

Thus, -3z = 6, and z = -2.

The solution set is (0, 3, -2). You should check this by substitution.

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3 years ago

The triangle below is equilateral. Find the length of side x to the nearest tenth.

Gemiola [76]

Answer:

$\sqrt{\frac{15}{2} }$ or 2.738

Step-by-step explanation:

Let’s just look at the triangle on the top with the $\sqrt{10}$ on the top and x on the bottom. (Basically the top half to the equilateral triangle)

There is a small square in the bottom right corner, which indicates that this triangle is a right triangle. This means that we can use the Pythagorean Theorem: $a^{2} +b^{2} =c^{2}$

We know that \sqrt{10} is our hypotenuse, and therefore our c in our equation. Let’s say that x=a in our equation. Therefore we are left to find b. However, b is half the length of the side of the original equilateral triangle. An equilateral triangle means that all three sides are the same length. Therefore our side would also be \sqrt{10} units long. However we know that b is half of that value, so b= $\frac{1}{2}(\sqrt{10})$ or $\frac{\sqrt{10} }{2}$