**I/GCSE Mathematics**** Question Analysis Topic: Mathematics - Probability**

A coin is tossed 5 times. Find the probability of getting (i) at least 4 heads, and (ii) at most 4 heads.

**Answer:**

I/GCSE Mathematics also covers the topic of probability.

When a coin is tossed five times:

There are 2^5 = 32 possible outcomes.

(i) Getting at least 4 heads is a combination of two scenarios; either getting 4 heads or 5 heads.

*(For better understanding, imagine a binary system where 1 stands for heads, 0 for tails.)*

Number of ways of getting 4 heads = 5, i.e. 11110, 01111. 10111, 11011, 11101

Number of ways of getting 5 heads = 1

Therefore the probability of getting at least four heads is (5+1)/32 = 6/32 = 3/16

(ii) Getting at most 4 heads is the total minus getting 5 heads.

The number of ways of getting 5 heads is one.

Therefore the probability of getting 5 heads is 1/32.

Hence, the probability of getting at most 4 heads is 1 - probability of getting 5 heads = 1 - 1/32 = 31/32

Remember for your I/GCSE Mathematics examination that other probability questions utilise not only coins as the scenario but cards and dice, too. Revise well!

End of analysis. Now flip a coin - heads, you continue studying; tails, you get to take a break!