Question

(1 point) A bag contains 9 red marbles, 6 white marbles, and 7 blue marbles. You draw 4 marbles out at random, without replacement. What is the probability that all the marbles are red? The probability that all the marbles are red is | What is the probability that exactly two of the marbles are red? The probability that exactly two of the marbles are red is What is the probability that none of the marbles are red? The probability of picking no red marbles is

Answer 1

A.) 4 marbles are drawn without replacement hence

1st marble is red P(A)=9/22=0.409

2nd marble also red (P(B|A)=8/21=0.381

3rd marble is red hence P= 7/20=0.35

Last marble is also red P= 6/19=0.316 hence the probability that all four are red= 0.409×0.381×0.35×0.316= 0.0172

B. Probability that exactly 2 marbles are red out of 4 hence again

Ist marble is red. P= 0.408

2nd is also red,P= 0.381

Now here comes three conditions, if 3rd and 4th are white then

P( 3rd is white)=6/20=0.3

P(4th is also white)= 5/19=0.273. Now the probability will be

P(R R W W)=0.408×0.381×0.3×0.273=0.0127

2nd condition

If first two are red and last two are blue then

P(3rd is blue)=7/20=0.35

P(4th is blue)=6/19=0.316, now the desired Probability as

P(R R B B)=0.408×0.381×0.35×0.316=0.0172

3RD condition

If first two are red and third is white and 4th is blue then

P(3rd is white)=6/20=0.3

P(4th is blue)=7/19=0.368

Now desired Probability is

P(R R W B)=0.0172 by multiplication

4th condition

If first 2 are red and 3rd is blue and 4th is white then

P(3rd is blue)=7/20=0.35

P(4th is white)=6/19=0.3158

Now P(R R B W)=0.0172

Now The Probability of at least 2 red is as

P(at least 2 red)=0.0172+0.0172+0.0172+0.0127=0.0643

C. P(No red) = 1-P(All red)=1-0.0172=0 .9828