Question

Suppose that a fair coin is tossed 10 times.

(a) What is the sample space for this experiment?

(b) What is the probability of at least two heads?

(c) What is the probability that no two consecutive tosses come up heads?

Answer 1

a) The sample space of this experiment would consist of 2¹⁰ that is 1024 elements, as each of the coin toss could result in either a head or a tail.

S = XXXXXXXXXX
P(X = H) = P(X = T) = 0.5

b) The number of heads in 10 coin tosses could be modelled here as:

Therefore 0.9893 is the required probability here.

c) Probability that no two consecutive tosses come up heads,

• There are 5 heads, This could happen in 2 ways only: HTHTHTHTHT or THTHTHTHTH
• There are 4 heads, Here, we need to fit 4 heads in 5 positions in between 6 tails that is in 5c4 = 5 ways
• similarly for 3 heads, 6c3 = 20 ways
• 2 heads: 7c2 = 21 ways
• 1 head: 8 ways

Total ways: 2 + 5 + 20 + 21 + 8 = 56 ways

Therefore probability = 56*0.5¹⁰ = 0.0546875