Question

probability

	Strawberry(S)	Chocolate(L)	Vanilla(V)	Total
Icecream (I)	63	21	8	92
Cake (C)	5	34	9	48
	68	55	17	140

1. P(S)

2.P(I)

3.P(S | I)

4. S and I independent?

5. P(S & I)

6. P(S or I)

7. Multiplication rule for dependent P(V | C)

Answer 1

Probability	Strawberry(S)	Chocolate(L)	Vanilla(V)	Total
Icecream (I)	63	21	8	92
Cake (C)	5	34	9	48
Total	68	55	17	140

1.

P(S) = 68 / 140 = 0.486

2.

P(I) = 92 / 140 = 0.657

3.

P(S | I) = P( S and I ) / P(I) = 63 / 92 = 0.685

4.

If S and I are independent, then :

P(S and I ) = P(S)* P(I)

P(S and I) = 63 / 140 = 0.45

P(S)*P(I) = (0.486)*(0.657) = 0.319

Since, P(S and I) is not equal to P(S)*P(I)

S and I are not independent

5.

P(S & I) = 63 / 140 = 0.450

6.

P(S or I) = P(S) + P(I) - P(S and I) = 0.486 + 0.657 - 0.450 = 0.693

7.

P(V | C) = P(V and C) / P(C) = 9 / 48 =  0.188