# P1

## QUESTION: Lauren, Harriet, & Amira are all playing a game which continues until someone wins. Lauren says “I have a 40% chance of winning”, whilst Harriet says “I have a $\frac{1}{4}$ chance of winning”. Amira then claims that if the Lauren & Harriet are correct, she must have a 0.35 chance of winning. Work out if Amira’s statement is true.

ANSWER: We know their probabilities must add up to 1 to make Amira’s statement true. To add these values together, we must make them all share the same format. Here, we’re going to convert them all to percentages.

Firstly, we get that

$0.35=35\%$

Then, we get

$\frac{1}{4}=1\div4=0.25=25\%$

Now, we can add the three probabilities together:

$40\%+25\%+35\%=100\%=1$

They all add to 1, so Amira’s statement is correct.