Answer to Question #127770 in Statistics and Probability for King

Question

a) Bag A consists of 40 balls, 10% of them are red, the rest of them are blue. Bag B consists of 10 balls,
30% of them are red, the rest of them are blue.
A ball is taken at random from Bag A and put into Bag B. Then, a ball is then taken at random from
Bag B. Find the probability of having a red ball eventually.
b) 10% of the students in Malaysia use ClassWiz Calculator. 30% of the students in Singapore use
ClassWiz Calculator.
A student is chosen at random from Malaysia to further his/her studies in Singapore. Then, a student
is chosen at random from Singapore. Find the probability of having a student who uses ClassWiz
Calculator eventually.

Answer 1

a)

10%/100%=1/10,

1/10$\cdot$40=4 red balls in the bag A.

40-4=36 blue balls in the bag A.

30%/100%=3/10

3/10⋅10=3 red balls in the bag B.

10-3=7 blue balls in the bag B.

Let A be the event of having a red ball eventually.

Let B be the event that the ball was taken at random from Bag A is red.

Then

P(A)=P(A|B)P(B)+P(A|$\overline{B}$)P($\overline{B}$ )

P(B)=m/n

4 red balls in the bag A, so m=4.

Bag A consists of 40 balls, so n=40.

P(B)=4/40=1/10,

P($\overline{B}$)=1-P(B)=1=1/10=9/10.

P(A|B)=m/n,

3 red balls in the bag B, so m=3+1=4.

Bag B consists of 10 balls, so n=10+1=11.

P(A|B)=4/11.

P(A|$\overline{B}$)=m/n,

3 red balls in the bag B, so m=3,

Bag B consists of 10 balls, so n=10+1=11.

P(A|$\overline{B}$)=3/11.

P(A)=4/11$\cdot$1/10+3/11$\cdot$9/10=31/90.

The probability of having a red ball eventually is equal 31/90.

b)

Let A be the event that  the students in Malaysia use ClassWiz Calculator.

10%/100%=1/10.

P(A)=1/10.

Let B be the event that  the students in Singapore use ClassWiz Calculator.

30%/100%=3/10.

P(B)=3/10.

Let C be the event of having a student who uses ClassWiz Calculator eventually.

$P(C)=1-P(\overline{C})$

$P(\overline{C})$=$P(\overline{A})P(\overline{B})$

$P(\overline{A})=1-P(A)=1-1/10=9/10$

$P(\overline{B})=1-P(B)=1-3/10=7/10$

$P(C)=1-9/10\cdot7/10=1-63/100=37/100$

The probability of having a student who uses ClassWiz Calculator eventually is equal 37/100.