Question

write sample space of tossing two coin simultaneously and find the probability of getting at least one head​ .please help me fast

Answer 1

$\large\underline\purple{\bold{Solution :- }}$

Sample Space, when two coins are tossed is

S = {(H,H), (H,T), (T,H), (T,T)}

This implies, number of elements in Samlpe space

• n(S) = 4

Let E be the Event getting atleast one head.

• E = {(H,H), (H,T), (T,H)}

This implies, number of elements in favourable outcomes

• n(E) = 3

Thus,

We know,

$\rm\:Probability \: of \: an \: event =\dfrac{Number \: of \: favourable \: outcomes}{Total \: number \: of \: outcomes \: in \: sample \: space}$

or

$\rm : \implies \: P(E) \: = \: \dfrac{n(E)}{n(S)}$

where,

• P(E) = required probability of event
• n(E) = Number of elements in favourable outcomes
• n(S) = Number of total outcomes

Therefore, required probability is given by

$\rm : \implies \boxed{ \pink{\: P(E) \: = \: \dfrac{3}{4} }}$

Explore More :-

• The sample space of a random experiment is the collection of all possible outcomes.
• An event associated with a random experiment is a subset of the sample space.
• The probability of any outcome is a number between 0 and 1.
• If probability of event is 1, it is called Sure event.
• If probability of event is 0, it is called impossible event.
• The probabilities of all the outcomes add up to 1.
• The probability of any event A is the sum of the probabilities of the outcomes in A.