Question

In a box there are 4 black beads and 3 red beads. In another box there are 3 black beads and 5 red beads. if 1 bead each is taken from the boxes at random what is probability of getting
a)same colors b) different colors c) atleast one black bead​

Answer 1

Step-by-step explanation:

box1: box 2 :

black : 4 black : 3

red : 3 red : 5

probability of taking 1 bead from box1 and 1 bead from box2

a) of same color

case 1: black

1. taking 1black from box1 =4/7 and 1 black from box2 = 3/8

=4/7 × 3/8 = 3/14

case 2: red

taking 1red from box1 =3/7 and 1red from box2 =5/8

= 3/7 × 5/8=15/56

p(same color bead) = 3/14 + 15/56 = 12+15 /56= 27/56

b) different colors

case 1: black from box 1 and red from 2

black from 1 =4/7

red from 2= 5/8

=4/7 × 5/8= 5/14

case 2: red from 1 and black from 2

red from 1 =3/7

black from 2= 3/8

= 3/7 ×3/8 = 9/56

different colors = case 1 or case2

p(different color beads) = 5/14 + 9/56 = 25+9/56= 34/56

=17/28

c)at least one black

case 1: one is black and one is red I.e both different

from b)

probability(both different)= 17/28

case2: both beads are black

from a)case1

p(both black) =3/14

p(at least one black) = case1 or case2

= 17/28 + 3/14=17+6/28=23/28