Question

1)

Suppose a bag contains 50 red balls, 30 green balls and 20 blue balls.

(a) If you draw 2 balls at random without replacement, what is the probability that they are red and green?

(b) If you draw 3 balls at random without replacement, what is the probability that all 3 are of different colour?

(c) If you draw 3 balls at random without replacement, what is the probability that you draw at least 1 red ball?

2) A disease X has infected 1% of the total population. After a thorough testing of a large sample size, the accuracy of the test is given as follows: if a person is infected, it will alert ”positive” 99.5% of the time, and if a person is healthy, then it will alert ”negative” 99% of the time. If you took the test and it returned ”positive”, what is the probability that you are actually infected?

3) If you roll 3 dice, what is the probability that the sum of the face-up values is 5 or 6

Answer 1

0 We have bag containing Red balls = 50 30 Green balls = Blue balls a are red and 50 x 30 x 1 30 100 *99X98! 2 x 981 99 = 0.3030 n! (b we draw two balls at random without replacement then probability that they green (99) (30(20) (620) since more without replacement m! (n-x)! then probability that all 3 are m! - of different colour ) (30) (30 ('90) we draw 3 balls at random En.cn-1) -----12:1 50x30x20 = 50x30x20 100 x 99798 6 100 x 99 x 98497! 31 911 100. 539 = 0.1855 C if we draw 3 balls at random without replacement, then probability that we draw at least I red ball |- Probabili lity that there is no red ball

= - all three balls drawn are either ar blue green E1- 180°) ( 30410) (1930 150 ) 11 1 - 1 - 50! 3! * 47! 97 | *3! 100! (150) 50x49x40 = 1 - 100 x 99 x 98 4 33 11 29 = 0.8788 33 2 A disease x has infected 1% of the total population Let Ai be an went which denotes that a person have a disease X PLA) = 0ool P[tert alert poorlove) person is ampacted) = 0.995 P(tert alert Negative person is not infected) - 0.99 =2 P (test alert positivel person is not infeeled.) = 1-0.995 = 0.005

-1-0.99 PC test alert Megalive I person is infected') = 1 = 0.01 a person If n took the test and it returned " positive" then probebility Meet person echially anfertad PC person is infected). P[test alert positive /person is infected) + f(person is not infected) - P(test olert poslive I person is not infected) 0.01% 0.995 + (1-0.01)(0.005) s 0.0149 w Cases if we we rol 3 dice then total number of outcomes in sample space in exaustive number = 6 X 6 X 6 = 216 of then mumber of favourable cases (outcomes) whose sum of the faces is 5 or 6 for sum 5, outcomes are (1.1, 3), (1,2,2) (1,3,1) (2,1,2) (2,2,1) (311,1)

The sumb outcomes are - (1,1,4) (1,2,3) (1,3,2) (1,4,1) (2,1,3) ( 2, , 2) (2,3,1) (310,2) 1 3,2,1) (4,1,1) number of the total favourable cases for rum 5or 6 6+ 10 = 16 since there is not Common outcome required probability favourable cases Total Cases 11 16 216 2 27 = 10:0741