Question

There is a 50% chance that it will snow each of the next three days. Fay wants to know the probability that it will snow all three days. Explain how a fair coin can be used to simulate this situation

Answer 1

P=0.1250

Explanation:

-Given the probability of snowing each day is 0.5.

#The probability that it snows in the next 3 days is calculated as:

`P_(all)=P_1* P_2* P_3\\\\=0.5* 0.5* 0.5\\\\=0.1250`

Hence, the probability that it snows in all 3 days is 0.125

#illustrating using a fair coin:

-A fair coin has two faces

-Each face has an equal probability

-If the coin is tossed 3 times, the sample space can be written as:

`C_(ss)=TTT, HTT, THT, TTH, HHT, HTH, THH, HHH.`

#The sample space is 8.

#Assuming that our event is 3 consecutive heads or 3 consecutive tails, the probability will be:

`P=P_(HHH)=P_(TTT)=(1)/(8)=0.125`