Question:
A bag X contains 2 white and 3 black balls and another bag Y contains 4 white and 2 black balls. One bag is selected at random and a ball is drawn from it. Then, the probability of the chosen ball to be white is
A bag X contains 2 white and 3 black balls and another bag Y contains 4 white and 2 black balls. One bag is selected at random and a ball is drawn from it. Then, the probability of the chosen ball to be white is
Options:
- 14/15
- 2/15
- 8/15
- 7/15
- 14/15
- 2/15
- 8/15
- 7/15
Correct Answer: a)
Explanation:
i A white ball can be drawn in two mutually exclusi√e ways:
1 i. Selecting bag X and then drawing a white ball from it.
‘ ii. Selecting bag Y and then drawing a white ball from it.
hon a
‘ Let Eq, Ep and A be three e√ents as defined below: ‘
‘ E = Selecting bag X
1 Ej = Selecting bag Y
‘ A = Drawing a white ball ‘
‘ We know that one bag is selected randomly. ‘
SPE) =3
—1
1 PED) 2 1
A) 2
P(#) =s
A) _4_2
P (#) —5 3
‘ Using the law of total probability, we get
1 PA) =2×2+ix2
1 =3+3 ‘
1119.
1
5
‘
i A white ball can be drawn in two mutually exclusi√e ways:
1 i. Selecting bag X and then drawing a white ball from it.
‘ ii. Selecting bag Y and then drawing a white ball from it.
hon a
‘ Let Eq, Ep and A be three e√ents as defined below: ‘
‘ E = Selecting bag X
1 Ej = Selecting bag Y
‘ A = Drawing a white ball ‘
‘ We know that one bag is selected randomly. ‘
SPE) =3
—1
1 PED) 2 1
A) 2
P(#) =s
A) _4_2
P (#) —5 3
‘ Using the law of total probability, we get
1 PA) =2×2+ix2
1 =3+3 ‘
1119.
1
5
‘