Answer:
60% of the employees are men.
Then the 40% left must be women.
4 of them are selected.
a) What is the random variable we can consider here?
A random variable is a variable that can have different outcomes or values, in other words, it is a stochastic variable.
We have a selection of 4 employees at random, then we can define the variable X, that represents (for each employee) the possibility of being man or woman.
b) Probability of 3 men and 1 woman.
Suppose that the selection is in the order:
man-man-man-woman.
We have:
0.6 tree times.
0.4 one time.
P = 0.6^3*0.4
But this is for the case where the woman is in the last selection, it can be in the first, second and third, then we have 4 permutations, the actual probability is:
P = 4*( 0.6^3*0.4) = 0.3456.
c) If now we have tat 75% are men, then 25% are women.
Now we can do the same as before, but now the probability for a man is 0.75 and for a woman is 0.25, then the previous equation is now:
P = 4*(0.75^3*0.25) = 0.421875
(a) The random variable will be "Men percentage".
(b) The probability of finding 3 men and one woman be "0.3456".
(c) The probability be "0.4219".
(a) A random variable represents a variable which might have several occurrences as well as quantities; it is indeed a stochastic quantity.
If we choose four workers at random, users may create the variable X, which reflects the potential of someone being a male or even a woman.
(b) The probability be:
→ P(3 men and women) = [tex]4C_3[/tex] (0.6)³ (1 - 0.6)¹
= 0.3456
(c) The probability be:
→ P(3 men and women) = [tex]4C_3[/tex] (0.75)³ (1 - 0.75)¹
= 0.4219
Thus the response above is correct.
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