Question

Use the formula for the probability of the complement of an event.A coin is flipped 4 times. Let E be the event of getting at least 1 head.Which of the following describes the event Ec?A) getting exactly 1 headB) getting at most 1 head C) getting at most 2 headsD) getting no headsHow many elements are in the event Ec? _______P(Ec)= ______P(E)= ______

Answer 1

ANSWER:

D) getting no heads

16 elements

P(Ec) = 1/16

P(E) = 15/16

STEP-BY-STEP EXPLANATION:

We have the following:

A coin is flipped 4 times.

The probability of head is the same as tail, in both cases it is 0.5.

$P(head)=P(tail)=\frac{1}{2}$

The sample space or total number of possible outcomes are 2^4 or 16 outcomes. E is the event of getting at least 1 head.

Therefore, the complement of this event (Ec) would be of getting no heads. There is only one element in event Ec.

$\begin{gathered} P(E^C)=P(0\text{ head})=P(4\text{ tails}) \\ P(E^C)=\frac{1}{2}\cdot\frac{1}{2}\cdot\frac{1}{2}\cdot\frac{1}{2}=\frac{1}{16} \end{gathered}$

Using the formula for probability of complement of an event

$\begin{gathered} P(E^C)+P(E^{})=1 \\ P(E^{})=1-P(E^C) \\ P(E^{})=1-\frac{1}{16}=\frac{15}{16} \end{gathered}$