Sherry Becker

2021-11-29

Give full and correct answer to the question, which of the following values cannot be​ probabilities? $.06,-0.4,11,0,\frac{3}{5},1.4,\frac{5}{3},\sqrt{2}$

Rosemary McBride

Concept of probability:Probability deals with the likelihood of occurrence of a given event. The probability value lies between 0 and 1. An event with probability 1 is considered as certain event and an event with probability 0 is considered as an impossible event. The probability of 0.5 infers of having equal odds of occurring and not occurring of an event.
The general formula to obtain probability of an event A is,
P(A) = (number of favorable elements for event A)/(Total number of elements in the sample space).
The basic properties of probability are given below:
$p=P\left(A\right)=\frac{n\left(A\right)}{n\left(S\right)}$
$0\le p\le 1$
Find the values that cannot be probabilities: The given values are 0.06, –0.4, 11, 00, 3/5, 1.4, 5/3 and $\sqrt{2}$.Since, 0.06 lies between 0 and 1, the value 0.06 can be probability.
Since, –0.4 is a negative value and does not lie between 0 and 1, the value –0.4 cannot be probability.
Since, 11 is greater than 1 and does not lie between 0 and 1, the value 11 cannot be probability.Since, 00 lies between 0 and 1, the value 00 can be probability.
Since, 3/5 = 0.6 lies between 0 and 1, the value 0.6 can be probability.
Since, 1.4 is greater than 1 and does not lie between 0 and 1, the value 1.4 cannot be probability.
Since, 5/3 = 1.6667 is greater than 1 and does not lie between 0 and 1, the value 1.6667 cannot be probability.
Since, $\sqrt{2}$ = 1.414 is greater than 1 and does not lie between 0 and 1, the value 1.6667 cannot be probability.Thus, the values –0.4, 11, 1.4, 5/3, $\sqrt{2}$ cannot be probabilities.

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