Probability of Getting Head or 4: 7/12

[alijan kk]

Homework Statement

If a coin flipped and one die is thrown, what is the probability of getting a head or a 4 ?

Homework Equations

The Attempt at a Solution

Sample Space={ H,1 H,2 H,3 H,4 H,5 H,6 T,1 T,2 T,3 T,4 T,5 T,6 }
Event={ H,1 H,2 H,3 H,5 H,6 T,4 }
probability is 6/12

if i don't do it with the formula P(A)+P(B)-P(AintersectionB)

i know the probability is 7/12

but what does probability of " a head or a 4" really mean ? should i add H,4 in the set of event but why it is necessary if yes

 

[Mark44]

Homework Statement

If a coin flipped and one die is thrown, what is the probability of getting a head or a 4 ?

Homework Equations

The Attempt at a Solution

Sample Space={ H,1 H,2 H,3 H,4 H,5 H,6 T,1 T,2 T,3 T,4 T,5 T,6 }
Event={ H,1 H,2 H,3 H,5 H,6 T,4 }

You left out the event H, 4.

probability is 6/12

if i don't do it with the formula P(A)+P(B)-P(AintersectionB)

i know the probability is 7/12

but what does probability of " a head or a 4" really mean ? should i add H,4 in the set of event but why it is necessary if yes

From the other thread you started (now deleted):

but what does probability of " a head or a 4" really mean ? should i add H,4 in the set of event but why it is necessary if yes

Yes you should add H, 4 to the events you're looking at. "A head or a 4" means that the coin turned up with a head OR the 4 on the die was on top OR both.

 

[alijan kk]

You left out the event H, 4.

H or 4 does that not mean either H or either 4 ? what is the difference in " H and 4 "

 

[Mark44]

H or 4 does that not mean either H or either 4 ? what is the difference in " H and 4 "

No, "or" here does not mean "either H or 4." It includes the possibility of both occurring.
So P(H or 4) consists of the events {(H, 1), (H, 2), (H, 3), (H, 4), (H, 5), (H, 6), (T, 4)}.
P(H and 4) consists of only one event: {(H, 4}}.

 

[alijan kk]

No, "or" here does not mean "either H or 4." It includes the possibility of both occurring.
So P(H or 4) consists of the events {(H, 1), (H, 2), (H, 3), (H, 4), (H, 5), (H, 6), (T, 4)}.
P(H and 4) consists of only one event: {(H, 4}}.

Thanks again <3

 

[hyunxu]

but what does probability of " a head or a 4" really mean ?
Don't get confuse .Be clear with event.
P (AUB) = P (A)+P (B)- P (A intersection B)
Use this formula if A intersects B.

P (AUB) = P (A)+P (B) => use this formula if A does not intersect B.