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?

a)0.25

b)0.14

Step-by-step explanation:

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

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

fist on the left goes with the third on the right. second on the left goes with the fourth on the right. third on the left goes with the second on the right. the fourth on the left goes with first on the right