Question

Suppose a coin is tossed ten times in a row with equal probability of heads and tails. a. What is the probability that heads never shows twice in a row? That is, with ten tosses, what is the probability heads never follows heads?

Answer 1

a)0.25

b)0.14

Explanation:

a) The event means tails shows for both coin toss. Then the probability of the event is:

`P(x)=0.5*0.5=0.25`

b)Possible number of patterns (total number of combinations) 2^n (each time either H or T=2 outcomes, 10 times=2^n).

Let's check two consecutive H:

If we toss once we'll have 2^1=2 combinations: H, T - 2 outcomes with NO 2 consecutive H.

If we toss twice we'll have 2^2=4 combinations: HT, TH, TT, HH - 3 outcomes with NO 2 consecutive H.

If we toss 3 times we'll have 2^3=8 combinations: TTT, TTH, THT, HTT, HTH, HHT, THH, HHH 5 outcomes with NO 2 consecutive H.

If we toss 4 times we'll have 2^4=16 combinations:... 8 outcomes with NO 2 consecutive H.

On this stage we can see the pattern in "no consecutive H": 2, 3, 5, 8... It's Fibonacci type of sequence and it will continue: 2, 3, 5, 8, 13, 21, 34, 55, 89, 144.

144 is outcomes with no consecutive H if we toss 10 times.

P(no two consecutive H in 10 toss)=144/2^10=144/1024=0.14