Question

A fair coin is tossed 10 times. What is the probability that two heads do not occur consecutively?

Answer 1

Answer:

0.140625

Step-by-step explanation:

Total numbers of possible combinations for a coin = 2^n

If the coin is tossed 10 times, we have 2^10 = 1024

If the coin is tossed once, we have 2^1 = 2 outcomes.

The possible outcomes are H, T.

We have 2 outcomes with no two consecutive head.

If the coin is tossed twice, we have 2^2 = 4 outcomes.

The possible outcomes are HH, HT, TH, TT

We have 1 outcome with two consecutive heads and 3 outcomes without two consecutive heads.

If the coin is tossed thrice, we have 2^3 = 8 outcomes.

The possible outcomes are HHH, HHT, HTH, HTT, TTH, THT, THH and TTT

We have 3 outcomes with two consecutive head and 5 outcomes without two consecutive heads.

Comparing the results from the outcomes of the coin,we have 2,3,5,......

This looks like a financial sequence. For the next 10 tosses, we have

2,3,5,8,13,21,34,55,89,144

We have 144 outcomes without two consecutive heads if the coin is tossed 10 times

Pr(number of two consecutive Heads in 10 tosses) = 144/1024

= 0.140625