Question

Q3. Two coins are thrown at the same
time. Find the probability of getting
both heads.
(A) 3/4
)
O (B)1/4
O (C) 1/2
(D) 0​

Answer 1

Answer:

1/4

Step-by-step explanation:

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Answer 2

Answer:

When two coins are tossed, sample space S is given by {HH,HT,TH,TT} and therefore, n(S)=4.

Let A denote the event that both head appear that is {HH} and n(A)=1, therefore, probability of both head appear is:

P(A)=n(S)n(A)=41

Let B denote the event that both tail appear that is {TT} and n(B)=1, therefore, probability of both tail appear is:

P(B)=n(S)n(B)=41

Intersection of A and B is the common elements between A and B which is none, thus, n(A∩B)=0 and 

P(A∩B)=n(S)n(A∩B)=40=0

Therefore, the events are mutually exclusive.

The probability of either both head or both tail occur is P(A∪B) and we know that for mutually exclusive event, P(A∪B)=P(A)+P(B) that is:

P(A∪B)=P(A)+P(B)=41+41=42=21

Hence, probability that either both heads or both tails occur is 21.