Question

What does at least mean in probability?

Answer 1

Key words meaning used in Probability:

The meaning of at least is Less than or equal to.

In probability, at least mean the minimum value that should occur once a random event happens.

Example: We throw $2$ dice, then the probability of the sum of two numbers is at least $7$ will be:

$\mathbf{\text{Probability}}\mathbf{=}\frac{\mathbf{\text{favourable outcomes}}}{\mathbf{\text{total outcomes}}}$

The possible total outcomes are:

$\left(1,1\right),\left(1,2\right),\left(1,3\right),\left(1,4\right),\left(1,5\right),\left(1,6\right),\left(2,1\right),\left(2,2\right),\left(2,3\right),\left(2,4\right),\left(2,5\right),\left(2,6\right),\left(3,1\right),\left(3,2\right),\left(3,3\right),\left(3,4\right),\left(3,5\right),\left(3,6\right)$

$\left(4,1\right),\left(4,2\right),\left(4,3\right),\left(4,4\right),\left(4,5\right),\left(4,6\right),\left(5,1\right),\left(5,2\right),\left(5,3\right),\left(5,4\right),\left(5,5\right),\left(5,6\right),\left(6,1\right),\left(6,2\right),\left(6,3\right),\left(6,4\right),\left(6,5\right),\left(6,6\right)$

The possible values where the sum of two numbers is at least $7$ are:

$\left(1,6\right),\left(2,5\right),\left(2,6\right),\left(3,4\right),\left(3,5\right),\left(3,6\right),\left(4,3\right),\left(4,4\right),\left(4,5\right),\left(4,6\right),\left(5,2\right),\left(5,3\right),\left(5,4\right),\left(5,5\right),\left(5,6\right),\left(6,1\right),\left(6,2\right),\left(6,3\right),\left(6,4\right),\left(6,5\right),\left(6,6\right),$

$P(\mathrm{the}\mathrm{sum}\mathrm{of}\mathrm{two}\mathrm{numbers}\mathrm{is}\mathrm{at}\mathrm{least}7)=\frac{21}{36}=\frac{7}{12}$.

Hence, the meaning of atleast word is defined