A Jar has 20 marbles in it 5 of which are yellow the rest gr

A Jar has 20 marbles in it, 5 of which are yellow, the rest green. You are selecting 6 at a time. What is the probability that:

1. you get exactly 1 yellow?

2. Probability at least 2 are yellow =

Solution

Solutions:

total marbles = 20

yellow marbles=5

Green marbles=20-5=15

total outcomes=20_C6

Selecting 6 marbles at at time ot of 20.its a combination.

exactly 1 yellow?

we have 5 yellow marbles out of which onne marble is yellow.so 5C1 and rest 5 are green 15

P(exactly one yellow)= 5_C1 15_C5 /20_C6 =5 * 3003/38760 =0.3873=38.73%

Atleast 2 yellow means there can be combinations of

2Y and 4G

3Y and 3G

4Y and 2G

5Yand 1G

Probability( at least 2 are yellow )=    5C2 *15C4+ 5C3 *15C3+5C4 *15C2 +5C5 *15C1/20_C6

   ₌10 *1365 +10*455 +5 *105 +1 *15/38760

=18740/38760

=0.4835

Probability at least 2 are yellow =48.35%