Find the sample space for choosing a prime number less than 2020 at random.
- A2, 3, 5, 7, 11, 13, 17, 19
- B2, 3, 4, 5, 7, 11, 13, 17, 19
- C2, 3, 5, 7, 11, 13, 17, 19, 20
- D2, 3, 5, 7, 11, 13, 17, 19, 15
Find the sample space for choosing a prime number less than 2020 at random.
Solution:
Sample space is the collection of all possible events.
So, sample space for choosing a prime number less than 20 = 2, 3, 5, 7, 11, 13, 17, 19.
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If $\text{f}(\text{x})=\begin{cases}\text{x}^{2}-1 & 0<\text{x}<2\\2\text{x}+3, & 2\geq\text{3}<3\end{cases}$ then the quadeatic equation whose roots are $\lim\limits_{\text{x} \rightarrow 2^{-}}\text{f}(\text{x})$ and $\lim\limits_{\text{x} \rightarrow 2^{+}}\text{f}(\text{x})$ is:
$\text{x}^{2}-6\text{x}+9=0$
$\text{x}^{2}-7\text{x}+8=0$
$\text{x}^{2}+14\text{x}+49=0$
$\text{x}^{2}-10\text{x}+21=0$
Given 5 different green dyes, four different blue dyes and three different red dyes, the number of combinations of dyes which can be chosen taking at least one green and one blue dye is.
[Hint: Possible numbers of choosing or not choosing 5 green dyes, 4 blue dyes and 3 red dyes are 25 , 24 and 23 , respectively.]