three coins are tossed simultaneously find the probablity of getting
(i) at least tail (ii) at most head (iii)all head
Answers
Answer:
When three coins are tossed together, the total number of outcomes =8
i.e., (HHH,HHT,HTH,THH,TTH,THT,HTT,TTT)
Solution (i):
Let E be the event of getting exactly two heads
Therefore, no. of favorable events, n(E)=3(i.e.,HHT,HTH,THH)
We know that, P(E) =
(Total no.of possible outcomes)
(No.of favorable outcomes)
=
8
3
Solution (ii):
Let F be the event of getting atmost two heads
Therefore, no. of favorable events, n(E)=7(i.e.,HHT,HTH,TTT,THH,TTH,THT,HTT)
We know that, P(F) =
(Total no.of possible outcomes)
(No.of favorable outcomes)
=
8
7
Solution (iii):
Let H be the event of getting at least one head and one tail
Therefore, no. of favorable events, n(H)=6(i.e.,HHT,HTH,THH,TTH,THT,HTT)
We know that, P(H) =
(Total no.of possible outcomes)
(No.of favorable outcomes)
=
8
6
=
4
3
PLEASE MARK IT AS BRAINLIST
Step-by-step explanation:
When three coins are tossed together, the total number of outcomes =8
i.e., (HHH,HHT,HTH,THH,TTH,THT,HTT,TTT)
Solution (i):
Let E be the event of getting exactly two heads
Therefore, no. of favorable events, n(E)=3(i.e.,HHT,HTH,THH)
We know that, P(E) =
(Total no.of possible outcomes)
(No.of favorable outcomes)
=
8
3
Solution (ii):
Let F be the event of getting atmost two heads
Therefore, no. of favorable events, n(E)=7(i.e.,HHT,HTH,TTT,THH,TTH,THT,HTT)
We know that, P(F) =
(Total no.of possible outcomes)
(No.of favorable outcomes)
=
8
7
Solution (iii):
Let H be the event of getting at least one head and one tail
Therefore, no. of favorable events, n(H)=6(i.e.,HHT,HTH,THH,TTH,THT,HTT)
We know that, P(H) =
(Total no.of possible outcomes)
(No.of favorable outcomes)
=
8
6
=
4
3
PLEASE MARK IT AS BRAINLIST
PLEASE MARK IT AS BRAINLIST
Step-by-step explanation:
Given: Three coins are tossed simultaneously.
When three coins are tossed then the outcome will be
TTT, THT, TTH, THH. HTT, HHT, HTH, HHH.
Hence total number of outcome is 8.
(i) For exactly two head we get favorable outcome as THH, HHT ,HTH
So, total number of favorable outcome i.e. exactly two head 3
We know that;
Probability =
N
u
m
b
e
r
o
f
f
a
v
o
r
a
b
l
e
e
v
e
n
t
T
o
t
a
l
n
u
m
b
e
r
o
f
e
v
e
n
t
Hence probability of getting exactly two head is
3
8
(ii) In case, at least two head we have favorable outcome as HHT, HTH, HHH ,THH
So, total number of favorable outcome i.e. at least two head is 4
We know that;
Probability =
N
u
m
b
e
r
o
f
f
a
v
o
r
a
b
l
e
e
v
e
n
t
T
o
t
a
l
n
u
m
b
e
r
o
f
e
v
e
n
t
Hence, probability of getting at least two head when three coins are tossed simultaneously is equal to
4
8
=
1
2
(iiii) At least one head and one tail we get in case THT, TTH, THH. HTT, HHT, HTH,
So, total number of favorable outcome i.e. at least one tail and one head is 6
We know that;
Probability =
N
u
m
b
e
r
o
f
f
a
v
o
r
a
b
l
e
e
v
e
n
t
T
o
t
a
l
n
u
m
b
e
r
o
f
e
v
e
n
t
Hence, probability of getting at least one head and one tail is equal to
6
8
=
3
4
(iv) No tail i.e HHH
Hence, total number of favorable outcome is 1
We know that;
Probability =
Number
o
f
f
a
v
o
r
a
b
l
e
e
v
e
n
t /
T
o
t
a
l
n
u
m
b
e
r
o
f
e
v
e
n
t
Hence, probability of getting no tails is
1
8