Question

Move two choices to the blanks to correctly complete the sentences.

Answer 1

(A) There should have been 5 outcomes of HT

(B) The experimental probability is greater than the theoretical probability of HT.

Explanation:

Given

`S = \{HH,HT,TH,TT\}` -- Sample Space

`n(S) = 4` --- Sample Size

Solving (a); theoretical outcome of HT in 20 tosses

First, calculate the theoretical probability of HT

`P(HT) = (n(HT))/(n(S))`

`P(HT) = (1)/(4)`

Multiply this by the number of tosses

`P(HT) * n= (1)/(4) * 20`

`P(HT) * n= 5`

Solving (b); experimental probability of HT

Here, we make use of the table

`P(HT) = (n(HT))/(n(S))`

`P(HT) = (6)/(20)`

`P(HT) = 0.30` ---- Experimental Probability

In (a), the theoretical probability is:

`P(HT) = (1)/(4)`

`P(HT) = 0.25` ---- Experimental Probability

By comparison;

`0.30 > 0.25`