Roger will flip a coin 3 times. which 2 events are disjoint?

Answer with explanation:

The four Options provided are

A. Getting exactly 1 head and Getting at least 2 tails

B. Getting at least 1 head and Getting at least 1 tail

C. Getting exactly 1 head and Getting at least 1 tail

D.Getting at least 2 heads and Getting at least 2 tails

→When Roger will flip a coin three times,

Total Possible Outcome

      ={H H H, H H T, H T H, T H H,H T T, T H T,T T H,T T T}

⇒Two events are said to be Disjoint, if

P (A ∩ B)=0→→P(A∪B)=P(A) +P(B)

Now, we will start from option ,1 that among four options which events are Disjoint.

1.A=Probability of Getting Exactly 1 Head={ H T T, T H T,T T H}

B=Probability of Getting at least 2 tails={H T T, T H T,T T H,T T T}

A ∩ B={H T T, T H T,T T H}≠0

→P (A∩B)≠0,

So, the two events are not Disjoint.

2.A=Probability of Getting At least 1 Head= ={H H H, H H T, H T H, T H H,H T T, T H T,T T H}

B=Probability of Getting At least 1 tail ={T T T, H H T, H T H, T H H,H T T, T H T,T T H}

A ∩ B={H H T, H T H, T H H,H T T, T H T,T T H}≠0

→P (A∩B)≠0,

So, the two events are not Disjoint.

3.A= Probability of Getting exactly 1 head={H T T, T H T,T T H}

B=Probability of Getting at least 1 tail={T T T, H H T, H T H, T H H,H T T, T H T,T T H}

A ∩ B={H T T, T H T,T T H}=3≠0

⇒P (A∩B)≠0,

So, the two events are not Disjoint.

4. A=Probability of Getting at least 2 heads ={H H H, H H T, H T H, T H H}

B=Probability of Getting at least 2 tails ={H T T, T H T,T T H,T T T}

A ∩ B=0

,⇒P (A∩B)=0,

So, the two events are Disjoint.

Option D: Getting at least 2 heads and Getting at least 2 tails, is disjoint event.

→There is no need to find Probability.You can write directly,that is if , A ∩ B≠0, the events are not disjoint.