Question

It is estimated within a group of people that $80\%$ people have health insurance, $90\%$ people have tea in the morning, and $60\%$ people exercise regularly. Using the simulator that generates random three-digit numbers using digits from 0 through 9, work out the probability that the person chosen has health insurance, drinks tea in the morning, and exercises everyday.
Note: The ones place of a three-digit number and 1 through 6 represents people doing regular exercise.
The tens place of the three-digit number and 1 through 9 represents people who drink tea.
The hundreds place of the three-digit number and 1 through 8 represents people having health insurance.

Simulator:

842	242	075	572	711	632	874	576	641	884
833	415	871	381	335	984	652	495	663	426
415	323	904	784	947	546	236	316	565	631
693	696	726	714	226	265	815	835	235	051
654	814	895	824	424	425	152	531	078	998

• A. $96\%$
• B. $60\%$
• C. $84\%$
• D. $86\%$

Answer 1

The correct option is D $86\%$

Ones place of a three-digit number represents people who exercise everyday.

Since there is a $60\%$ chance of people exercising, let 1 through 6 represent a person who exercises everyday.

The tens place of the three-digit number represents people drinking tea in the morning.
Since there is a $90\%$ chance of a person drinking tea, let 1 through 9 represent people drinking tea.

The hundreds place of the three-digit number represents people having credit cards.
Since there is an $80\%$ chance of a person having a credit card, let 1 through 8 represent people having credit card.

From the simulation, we see that 43 out of 50 people have credit cards, drink tea in the morning, and also exercise everyday.
Estimated probability $=\frac{43}{50}\times 100=86\%$