Answer:
1) a) 0.0945
b) 0.1062
2) a) 0.0138
b) 0.00081
3) a) 0.00094
b) 0.00083
4) 301.68 cents
5) 0.0056
Step-by-step explanation:
Since there are 3 Red, 7 Green, and 10 Blue marbles.
Total number of marbles N = 20
Probability (Red) = 3/20
Probability (Green) = 7/20
Probability (Blue) = 10/20
1) the probability of picking 5 marbles and getting at least one red marble
A) with replacement
P(at least 1 red of 5)= (3/20 * 17/20 * 17/20 * 17/20 * 17/20) + (3/20 * 3/20 * 17/20 * 17/20 * 17/20) + (3/20 * 3/20 * 3/20 * 17/20 * 17/20)
P(at least 1 red of 5) = 0.0783 +0.0138 + 0.0024 = 0.0945
B) without replacement
P(at least 1 red of 5) = ( 3/20 * 17/19* 16/18 * 15/17 * 14/16) + (3/20 * 2/19 * 17/18 * 16/17 * 15/16) + (3/20 * 2/19 * 1/18 * 17/17 * 16/16)
P(at least 1 red of 5) = 0.0921 + 0.01316 + 0.0009 = 0.1062
2) the probability of picking 6 marbles having 2 of each color
A) with replacement
P( 6, 2 of each) = 3/20 * 3/20 * 7/20 * 7/20 * 10/20 * 10/20
P( 6, 2 of each) = 0.0138
B) without replacement
P( 6, 2 of each) = 3/20 * 2/19 * 7/18 * 6/17 * 10/16 * 9/15
P( 6, 2 of each) = 0.00081
3) Pick 8 marbles: 4 green and 4 blue
A) with replacement
P(8, 4G and 4 B) = 7/20*7/20*7/20*7/20*10/20*10/20*10/20
P(8, 4G and 4 B) = 0.00094
B) without replacement
P(8, 4G and 4 B) = 7/20*6/19*5/18*4/17*10/16*9/15*8/14*7/13 = 0.00083
4) getting at least 6 marbles of the same color
Only Green and Blue marbles are more than 6
P(at least 6 marbles of the same color) = (7/20*6/19*5/18*4/17*3/16*2/15) + (10/20*9/19*8/18*7/17*6/16*5/15)
= 0.00018 + 0.00542
P(at least 6 marbles of the same color) = 0.0056
Cost of 6 .marbles= 6* 50 cents
C = 300 cents
Therefore, You will have to pay
(1 + 0.0056) 300 cent = 301.68 cents to be sure of getting at least 6 marbles of the same color
5) getting at least 6 marbles of the same color
Only Green and Blue marbles are more than 6
P(at least 6 marbles of the same color) = (7/20*6/19*5/18*4/17*3/16*2/15) + (10/20*9/19*8/18*7/17*6/16*5/15)
= 0.00018 + 0.00542
P(at least 6 marbles of the same color) = 0.0056
