Three coins are tossed simultaneously What is the probability of getting : i) two heads ii) - Maths - Probability

Question

Three coins are tossed simultaneously What is the probability of
getting :
i) two heads ?
ii) at most one head ?
iii) atleast two heads ?
iv ) at most two heads ?
please solve the query soon Thank you

Manmeet Singh · Accepted Answer

Let H : Head and, T : Tail then the outcomes when 3 coins are tossed simultaneously are $\begin{matrix} H & H & H \\ H & H & T \\ H & T & H \\ H & T & T \\ T & H & H \\ T & H & T \\ T & T & H \\ T & T & T \end{matrix}$ Thus total outcomes are 8 (1) two heads means exactly 2 heads Favourable cases = (HHT, HTH, THH) Probability = $\frac{n u m b e r o f f a v o u r a b l e o u t c o m e s}{t o t a l n u m b e r o f o u t c o m e s} = \frac{3}{8}$ (2) at most one head means one head or no head Favourable cases = (HTT, THT, TTH, TTT) Probability = $\frac{n u m b e r o f f a v o u r a b l e o u t c o m e s}{t o t a l n u m b e r o f o u t c o m e s} = \frac{4}{8} = \frac{1}{2}$ (3) atleast two heads means two or three heads Favourable cases = (HHH, HHT, HTH, THH) Probability = $\frac{n u m b e r o f f a v o u r a b l e o u t c o m e s}{t o t a l n u m b e r o f o u t c o m e s} = \frac{4}{8} = \frac{1}{2}$ (4) atmost two heads means 0, 1 or 2 heads Favourable cases = (HHT, HTH, HTT, THH, THT, TTH, TTT) Probability = $\frac{n u m b e r o f f a v o u r a b l e o u t c o m e s}{t o t a l n u m b e r o f o u t c o m e s} = \frac{7}{8}$

Three coins are tossed simultaneously . What is the probability of getting : i) two heads ? ii) at most one head ? iii) atleast two heads ? iv ) at most two heads ? please solve the query soon . Thank you .

Three coins are tossed simultaneously . What is the probability of getting :

i) two heads ?

ii) at most one head ?

iii) atleast two heads ?

iv ) at most two heads ?

please solve the query soon . Thank you .