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3 years ago

If A and B are independent events, P(A and B) =

Mathematics

1 answer:

Sergio039 [100]3 years ago

4 0

Answer:

If A and B are independent events, P(A and B) = P (A) * P (B)

Step-by-step explanation:

Let's recall that independent events means that when one event occurs, it has no impact or influence on the probability of another event occurring. Here’s an example. Let’s say that we have two events, A and B.

Event A : it rains in Seattle

Event B : the Super Bowl match is cancelled in Miami

The two events are independent; if it rains in Seattle, this will have no impact on the probability that the Super Bowl match is cancelled in Miami. Raining in Seattle and the cancellation of the Super Bowl are independent events, therefore:

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

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Melanie has a $60 so far to buy a lawn mower. This is 20% of the price of the lawn mower. What is the full price of the lawn mow

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--Percent means out of 100, so 20% = 20/100

The prob in other words is asking
-- $60 is 20% of what number?

'$60'   -- ---> 60
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3 years ago

The lenght of a rectangle is 2 units more than the width. The area of the rectangle is 48 units. What is the length, in units, o

LenKa [72]

Answer:

The length of this rectangle is 6 units.

Step-by-step explanation:

Let the width of the rectangle be x.

x • (x+2) = 48

x^2+2x=48

x^2+2x-48=0

x^2 - 6x + 8x - 48

x(x-6) 8(x-6)

(x+8)(x-6)

x=-8,6

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3 years ago

Read 2 more answers

There are 3 red marbles, 5 green marbles, and 2 blue marbles in a jar. Event A is defined as drawing a red marble from the jar o

Anastaziya [24]

P(B/A) is $\frac{5}{9}$ in the simplest form

Step-by-step explanation:

Let us explain how to solve the problem

P(B|A) is called the "Conditional Probability" of B given A
Conditional probability is the probability of one event occurring with some relationship to one or more other events that means event A has already happened, now what is the chance of event B
The formula for conditional probability is P(B|A) = P(A and B)/P(A), where P(A and B) is P(A) . P(B given A occurred)

∵ There are 3 red marbles, 5 green marbles, and 2 blue

marbles in the jar

∴ The total number of the marbles in the jar = 3 + 5 + 2 = 10

∵ Two marbles are drawn from the bag, one after the other without

replacement

- That means red is already occurred when green is happened,

so it is a "Conditional Probability" of green given red

P(B/A) = P(A and B)/P(A)

∵ Event A is defined as drawing a red marble from the jar on

the first draw

∴ P(A) = P(red)

∵ P(red) = $\frac{3}{10}$

∴ P(A) = $\frac{3}{10}$

∵ Event B is defined as drawing a green marble on the second draw

∴ P(B) = P(green)

- The number of marbles after the red is chosen is 9

∵ P(green) = $\frac{5}{9}$

∴ P(B) = $\frac{5}{9}$

- Find P( A and B)

∴ P(A and B) = ( $\frac{3}{10}$ ) . ( $\frac{5}{9}$ )

∴ P(A and B) = $\frac{15}{90}$

- Simplify the fraction by divide up and down by 15

∴ P(A and B) = $\frac{1}{6}$

∵ P(B|A) = P(A and B)/P(A)

- Substitute the values of P(A and B) and P(A) in the rule above

∴ P(B/A) = $\frac{\frac{1}{6}}{\frac{3}{10}}$

- Simplify the fraction

∵ $\frac{1}{6}$ ÷ $\frac{3}{10}$ = $\frac{1}{6}$ × $\frac{10}{3}$ = $\frac{10}{18}$

- Divide up and down by 2

∴ P(B/A) = $\frac{5}{9}$

P(B/A) is $\frac{5}{9}$ in the simplest form

Learn more:

You can learn more about probability in brainly.com/question/10744457

#LearnwithBrainly

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ivann1987 [24]

Answer:

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Step-by-step explanation:

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3 years ago

If A and B are independent events, P(A and B) =​

If A and B are independent events, P(A and B) =