A fair coin is tossed 5 times. What is the probability of getting at least three heads on consecutive tosses?

Answer 1

5 tosses of a coin, at least 3 heads:

use formula nCr * Pⁿ * Q^n-q

At least 3 heads:

A. 3 heads, 2 tails or 

B. 4 heads, 1 tails, or 

C. 5 heads, 0 tails:

A. 

The set contains {hhhtt, tthhh, thhht, hhtth, hhtht,htthh,ththh,hthth,thhth,hthht} ... just info, calculate nCr:

Use 5C3=5!/2!3! = 5*4/2=10

B. 

The set contains {hhhht, hhhth,hhthh,hthhh,thhhh} ... just info

Use 5C4 = 5!/1!4! = 5

C.

The set contains {hhhhh} ... just info, calculate nCr:

Use 5C5 = 5!/0!5! = 1

So 10 ways or 5 ways or 1 way —> add all three or conditions:

Example 10 ways: 

   nCr * P(H) * P(H) * P(H) * P(not H) * P(not H),

   P(H) = 1/2, P(not H) = 1/2, nCr = 10

Total:

10 * (1/2)^3 * (1/2)^2 +

5 * (1/2)^4 * (1/2)^1 +

1 * (1/2)^5 * (1/2)^0

= 1/2