Respuesta :
Solution
- The information given to us can be written mathematically as:
[tex]\begin{gathered} P(calc)=\frac{4}{5} \\ P(no\text{ }calc)=1-\frac{4}{5}=\frac{1}{5} \end{gathered}[/tex]Question A:
- If two students are chosen at random and both of them have a calculator, this means that the probability of choosing the two of them is calculated by the AND formula.
- That is,
[tex]\begin{gathered} P(A)\text{ AND }P(B)=P(A)\times P(B) \\ \text{ Given that events A and B are independent events.} \\ \\ \text{ Since the selection of the two students is random, it means that the event of choosing} \\ \text{ the two students are independent, thus, we have:} \\ \\ P(both\text{ have calculator\rparen}=\frac{4}{5}\times\frac{4}{5}=\frac{16}{25} \end{gathered}[/tex]Question B:
- The probability that only one of them has a calculator implies that 1 has a calculator and the other does not have a calculator.
- Thus, we have:
[tex]\begin{gathered} P(1\text{ student with calc\rparen}\times P(1student\text{ without calc\rparen} \\ =\frac{4}{5}\times\frac{1}{5}=\frac{4}{25} \\ \\ \text{ But there are two possible scenarios:} \\ 1.\text{ we can either pick one student with a calculator first and then one with no calculator} \\ 2.\text{ We can also pick one with no calculator first, before picking one with a calculator} \\ \\ \text{ Thus, } \\ P(\text{ Only one has a calculator})=2\times\frac{4}{25}=\frac{8}{25} \end{gathered}[/tex]Final Answer
The answers are:
[tex]\begin{gathered} Question\text{ A:} \\ \frac{16}{25} \\ \\ Question\text{ B:} \\ \frac{8}{25} \end{gathered}[/tex]