Question

II
If an unbiased coin is tossed 5 times the probability of getting only one head is equal​

Answer 1

the probability of a head is p, then the probability of a tail is q = 1 -p.

The only event without a head is 5 tails, which occurs with probability q ^ 5.

If p = 1/2 (a fair coin), then q = 1 - 1/2 = 1/2, and the probability of getting at least one head is 1 - probability of 5 tails = 1 - (1/2)^5 = 1 - (1/31)= 31/32.

Answer 2

p= probability of getting head in one toss =
2
1
​

q=(1−p)=
2
1
​

x= no. of heads
∴p(x≥3)
=1−p(x≤2)
=1−p(x=0)−p(x=1)−p(x=2)
Now p(x=0)=
8
C
0
​
(
2
1
​
)
0
(
2
1
​
)
8

=(
2
1
​
)
8

p(x=1)=
8
C
1
​
(
2
1
​
)
1
(
2
1
​
)
7

=8×(
2
1
​
)
8

p(x=2)=
8
C
2
​
(
2
1
​
)
2
(
2
1
​
)
6

=
6!×2!
8!
​
×
2
8

1
​

=56×(
2
1
​
)
8

∴p(x≥3)=1−(
2
1
​
)
8
−8×(
2
1
​
)
8
−56(
2
1
​
)
8

=1−
2
8

65
​
.