Maths, probability

Question

'Milly has a biased coin.

When she throws the coin once, the probability of getting heads is 0.2.

The probability of getting tails is 0.8.

 

Milly throws the coin 200 times.

 

Work out the estimate for the number of times she gets heads.'

 

Thank you in advance.

Answer 1

Consider that word, "estimate." It means we do not expect our results to be absolutely true or trustworthy - only that they are the most correct results possible under the given circumstances. In this circumstance, we have a "biased" coin - meaning that the coin doesn't land with an equal chance for heads or tails. This coin apparently favors tails, but by how much?

 

Chance of Heads = 0.2

That's 20%.

Chance of Tails = 0.8 or 80%.

Aren't we far more likely to get Tails? But how much?

 

How many times does 20% divide into 80%? 80 divided by 20 is 4.

We expect Tails to come up 4 times as often as Heads. Or, said another way: we expect Tails to come up 4 times for every time Heads comes up.

 

Will this always be absolutely true - without exception - in any trial ever made using this coin? No! It is a mere expectation based upon probability.

 

One thing will always be absolutely true: all coin tosses, taken together, equal 100%! 20% Heads plus 80% Tails equals 100% of all coin tosses.

 

It is given here that Milly will toss the coin 200 times & we must predict how many times we can "expect" Heads. If Heads comes up 20 out of 100 tosses, how many Heads will you expect from 200 tosses?

 

Write this out, show your work, and solve it:

 

200 x 0.20 =