Question

Imagine flipping eleven fair coins.a. What is the theoretical probability that all eleven will come up tails?b. What is the theoretical probability the first toss is heads AND the next ten are tails?

Answer 1

a)

`(1)/(2048)`

b)

`(1)/(2048)`

Step-by-step explanation:

a) Given:

Flipping eleven fair coins

To find:

The theoretical probability that all eleven will come up tails

Recall the below probability formula;

`Probability=\frac{Number\text{ of favourable outcomes}}{Total\text{ number of possible outcomes}}`

If one fair coin is flipped, the total number of possible outcomes is 2 (HT) and the probability of obtaining a tail will 1/2.

So if eleven coins are flipped, the probability that all eleven will come up tails will be;

`P(all\text{ }eleven\text{ }will\text{ }come\text{ }up\text{ }tails)=((1)/(2))^(11)=(1^(11))/(2^(11))=(1)/(2048)`

So the probability that all eleven will come up tails is 1/2048

b) The probability that the first toss is head is;

`P(first\text{ toss is head\rparen }=(1)/(2)`

The probability that the next ten are tails will be;

`P(the\text{ }next\text{ }ten\text{ }are\text{ }tails)=((1)/(2))^(10)=(1^(10))/(2^(10))=(1)/(1024)`

Therefore the probability that the first toss is head AND the next ten are tails will be;

`P(first\text{ }toss\text{ }is\text{ }head\text{ }AND\text{ }next\text{ }ten\text{ }are\text{ }tails)=(1)/(2)*(1)/(1024)=(1)/(2048)`

So the probability that the first toss is head AND the next ten are tails is 1/2048