Probability

Question

A bag contains 15 identical marbles. There are 7 red, 3 blue and 5 yellow marbles. A marble is picked out at random and not replaced. A second marble is then picked out at random and not replaced. 

 

a) find the probability that

(i) both marbles are red 

(ii) one marble is red and the other is not red 

 

b) a third marble is now picked out at random. Calculate the probability that two marbles are red and one is not red. 

Answer 1

15 marbles, 7 red and 3 blue and 5 yellow

what is the probability that if you pick three marbles you get 2 red and 1 not red

here are the ways to pick the marbles:

RRN  where R=red and N=not red

NRR

RNR

P(RRN)+P(NRR)+P(RNR)=(7/15)((6/14)(8/13)+(8/15)(7/14)(6/13)+(7/15)(8/14)(6/13)=

you can simplify each product...

(1/5)(8/13)+(8/5)((1/13)+(1/5)(4/1)(2/13)=(8/65)+(8/65)+(8/65)=24/65

or,...

7*6*8=336 and 13*14*15=2730

(336/2730)*3=1008/2730=336/910=168/455=24/65 (168 and 455 are both divisible by 7)

24/65 is the answer to b)

Answer 2

(i) both marbles are red

 

p( 1st red marble) = 7/15

 

p( 2nd red marble) = 6/14

 

p (both red) = 7/ 15 * 6/14 = 1/5

 

(ii) one marble is red and the other is not red

p( one marble red) = 7/15

p( 2nd not red) =8/14

 

p(1st not red) = 8/15

p(2nd red) =7/14

 

p(( one marble is red and the other is not red ) = 7/15 * 8/14   +  8/15*7/14=  4/15  + 4/15 =8/15