In: Statistics and Probability
STAT 13_1:
A military company has three divisions. There are 20 soldiers in
each division. In divisions A - 4 female soldiers, in divisions B -
8 female soldiers and in divisions C - 12 female soldiers.
During one week, one of the divisions is chosen, incidentally, to
be the division that gives a watchman duty.
Each day, one of the soldiers of the selected division is randomly
selected to be the division watchman.
(The same soldier or female soldier may be selected for more than
one day)
A. What is the probability that on Sunday the division guard
will be a female-soldier?
B. Are the events "The selected division is division
B" and "On Sunday the Company Guard is a
female-Soldier" are independent events?
explain!
C. It is known that on Sunday and Monday, the division guard was a
female-soldier. What is the probability that the selected division
is C?
D. It is known that on Sunday and Monday the duty guard was a
female-soldier. What is the probability that on Tuesday the
division duty guard will be a soldier (man)?
(A)
From the given data, the following Table is calculated:
Male | Female | Total | |
A | 16 | 4 | 20 |
B | 12 | 8 | 20 |
C | 8 | 12 | 20 |
Total | 36 | 24 | 60 |
the probability that on Sunday the division guard will be a female-soldier = P(Female) = 24/60 = 0.4
(B)
The events "The selected division is division B" and "On Sunday the Company Guard is a female-Soldier" are independent events
Explanation:
P( The selected division is division B AND On Sunday the Company Guard is a female-Soldier ) = 8/60= 0.1333
P( The selected division is division B ) = 20/60 = 0.3333
P(On Sunday the Company Guard is a female-Soldier) = 24/60= 0.4
So,
P( The selected division is division B ) X P(On Sunday the Company Guard is a female-Soldier) = 0.3333 X 0.4 = 0.1333
Since P( The selected division is division B ) X P(On Sunday the Company Guard is a female-Soldier) = 0.3333 X 0.4 = 0.1333 = P( The selected division is division B AND On Sunday the Company Guard is a female-Soldier ) = 8/60= 0.1333, the events "The selected division is division B" and "On Sunday the Company Guard is a female-Soldier" are independent events
(C)
P(C/ Female) = P(C AND Female)/ P(Female)
= 12/24 = 0.5
So,
the probability that the selected division is C = 0.52 = 0.25
(D)
the probability that on Tuesday the division duty guard will be a soldier (man) = 36/60 = 0.6