The probability of rain in Greg’s town on Tuesday is 0.3. The probabil

Question

The probability of rain in Greg’s town on Tuesday is 0.3. The probability that Greg’s teacher will give him a pop quiz on Tuesday is 0.2. The events occur independently of each other. What is the probability that either or both events occur ?

A. 0.28
B. 0.32
C. 0.44
D. 0.56
E. 0.6

A. 0.28
B. 0.32
C. 0.44
D. 0.56
E. 0.6

sahuanamika · Answer

Let's say A event - raining so, P(A) = 0.3 
B event - Quiz so , P(B) = 0.2

P(A and B) = P(A)* P(B) as both are independent = 0.3*0.2 = 0.06
P(A or B) = P(A) + P(B) - P(A and B) 
P(A) = 0.3+0.2 - 0.06 = 0.44 
Ans C

Kinshook · Answer

Given: The probability of rain in Greg’s town on Tuesday is 0.3. The probability that Greg’s teacher will give him a pop quiz on Tuesday is 0.2. The events occur independently of each other.

Asked: What is the probability that either or both events occur ?

Event A: Rain in Greg’s town on Tuesday
Event B: Greg’s teacher will give him a pop quiz on Tuesday

P(A) = .3
P(B) = .2
P(A&B) = .3*.2 = .06
P(AUB) = .3 + .2 - .06 = .44

IMO C

unraveled · Answer

The most important part of the question is that the two events are independent. Thus, probability of them occurring together must be subtracted form the total of independent occurrence. 
P = 0.3+0.2 - 0.3*0.2 = 0.44

Answer C.

Adarsh_24 · Answer

Can we do 1-neither = 1-(.7 * .8) = .44 ?
My doubt is regarding multiplying probability of events not happening is possible if both events are independent.

I think it can. Since, in a vennn diagram it will be the intersection of outside A and outside B => Outside of both.

luisdicampo · Answer

Deconstructing the Question

We want the probability that  either or both  events occur.

Let  A  be the event that it rains on Tuesday, and let  B  be the event that Greg gets a pop quiz on Tuesday.

The key idea is to use the union formula:

P(A\cup B)=P(A)+P(B)-P(A\cap B)

Since the events are  independent , we can compute the overlap using multiplication.

Step-by-step

Let:

P(A)=0.3

and

P(B)=0.2

Because the events are independent:

P(A\cap B)=P(A)\cdot P(B)=0.3\cdot 0.2=0.06

Now apply the union formula:

P(A\cup B)=P(A)+P(B)-P(A\cap B)

=0.3+0.2-0.06

=0.44

So the probability that either or both events occur is  0.44 .

Answer: C) 0.44

SS3003 · Answer

How can either or both occur mean Either A or B occurs? Then how do we translate between the question Stem

Bunuel · Answer

The probability of rain in Greg’s town on Tuesday is 0.3. The probability that Greg’s teacher will give him a pop quiz on Tuesday is 0.2. The events occur independently of each other. What is the probability that either or both events occur ?

A. 0.28
B. 0.32
C. 0.44
D. 0.56
E. 0.6

A. 0.28
B. 0.32
C. 0.44
D. 0.56
E. 0.6

“Either or both” means at least one event occurs.

Use:

P(rain or quiz) = P(rain) + P(quiz) - P(both)

Since the events are independent:

P(both) = 0.3 * 0.2 = 0.06

So:

0.3 + 0.2 - 0.06 = 0.44

Answer: C.

“Either or both” means  at least one  of the two events occurs.

So it includes three cases:

Rain only
Quiz only
Both rain and quiz

It excludes only one case:

Neither rain nor quiz

So in probability language, the stem is asking for:

P(rain or quiz)

Here, “or” is  inclusive , not exclusive. If the question wanted only one event but not both, it would say  “either rain or quiz, but not both.”

SS3003 · Answer

Thank you , one more follow up question- How will the probability of "either rain or test not both" be different from "either or both". For either rain or test not both too we would use P(rain) +P(test) - P( rains AND test)

Bunuel · Answer

No.

P(rain) + P(quiz) - P(both) gives “rain or quiz or both.” It includes the case in which both happen. That is because P(rain) includes the “both” case once, and P(quiz) also includes the “both” case once. So when we subtract P(both) once, the “both” case is still counted once.

For “rain or quiz, but  not  both,” we must exclude the “both” case entirely:

P(rain only) + P(quiz only) =

= 0.3 * 0.8 + 0.2 * 0.7 =

= 0.24 + 0.14 =

= 0.38

Equivalently:

P(rain) + P(quiz) - 2P(both) =

= 0.3 + 0.2 - 2(0.06) =

= 0.38

We subtract 2P(both) because P(rain) includes the “both” case once, and P(quiz) also includes the “both” case once. Since “rain or quiz, but not both” excludes that case completely, we need to subtract it twice.

The probability of rain in Greg’s town on Tuesday is 0.3. The probabil

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The probability of rain in Greg’s town on Tuesday is 0.3. The probabil

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