Hard probability

Hi,

# of ways of getting exactly 3 heads = 5C3 = 10

# of ways of getting exactly 4 heads = 5C4 = 5

# of ways of getting exactly 5 heads = 5C5 = 1

# of ways of getting at least 3 heads = 10 + 5 + 1 = 16

Total # of ways of getting outcomes = 2 power 5 = 32.

Hence, probability = 1/2.

Hope this helps. Thanks.

duongthang wrote:what is probability of getting at least 3 heads when flipping 5 coins

General coin flip strategy,
https://www.beatthegmat.com/coin-flip-qu ... 17911.html

We can also arrive at the answer through reasoning. With 5 flips the following outcomes will have the same probability:

>> All heads = All tails
>> 1 tail & 4 heads = 1 head & 4 tails
>> 2 tails & 3 heads = 2 heads & 3 tails

Probability of at least 3 heads is the sum of all the probabilities on the left side (3 or 4 or all heads). This must equal the sum of probabilities on the right side. Since all outcomes must have a combined probability of 1, the sum of each side must be 1/2.

P (at least 3 heads) = 1/2