Question

Given an experiment in which a fair coin is tossed four times, the sample space is S = {HHHH, HHHT, HHTH, HHTT, HTHH, HTHT, HTTH, HTTT, THHH, THHT, THTH, THTT, TTHH, TTHT, TTTH, TTTT}. Define event A as tossing four heads. What is the event Ac and what is the probability of this event?

Answer 1

The event Ac represents the complement of event A, which includes all outcomes in the sample space that are not in event A. The probability of event Ac is 1.

Step-by-step explanation:

The event Ac represents the complement of event A, which means it includes all outcomes in the sample space S that are not in event A. In this case, event Ac would include all outcomes that do not have four heads. Since event A represents tossing four heads, the outcomes in event Ac would be {TTTT, TTTT, TTTT, TTTT, TTHH, TTHT, TTTH, TTTT, HTTT, THHT, THTH, TTTT, HHTT, HTTH, HTHT, HTTT}.

To find the probability of event Ac, we need to calculate the number of outcomes in event Ac and divide it by the total number of outcomes in the sample space. In this case, there are 16 outcomes in event Ac, and the total number of outcomes in the sample space S is 16. Therefore, the probability of event Ac is 16/16 = 1.

Answer 2

`P(A^c)=(15)/(16)`

Step-by-step explanation:

The sample space of a coin tossed four times is given below:

S = {HHHH, HHHT, HHTH, HHTT, HTHH, HTHT, HTTH, HTTT, THHH, THHT, THTH, THTT, TTHH, TTHT, TTTH, TTTT}.

n(S)=16

Event A is the event of Tossing four heads.

The Event
`A^c`, the Complement of A is the event of not tossing four heads.

`P(A)=(n(A))/(n(S))=(1)/(16) \\Therefore:\\P(A^c)=1-P(A)\\=1-(1)/(16) \\=(15)/(16)`