marbles question math

Question

bag contains 10 red marbles, five white marbles, eight blue marbles. you draw out five marbles out of random without replacement. what is the probability that all the marbles are red? and what is the probability that exactly two of the marbles are red. and what is the probability that none of the marbles are red

Answer 1

5+8+10= 23 total marbles

10 are red

5 white

8 blue

draw 5 randomly

probability 1st is red = 10/23

2nd red odds = 9/22

P(3rd red) = 8/21

P(4th)= 7/20

P(5th)= 6/19

probability of 5 red in a row, without replacement

= (10/23)(9/22)(8/21)(7/20)(6/19)

=(10!/5!)(18!/23!)=10!18!/5!23!

multiply the 5 fractions together

10x9x8x7x6/23x22x21x20x19

= about .0075

= about 0.75%

which is less than 1% chance

! means factorial, as a symbol the same as an exclamation mark

Probability none are red = (13/23)(12/22)(11/21)(10/20)(9/19)

= 13!/8! x 18!/23!

= about .038= 3.8%=

about 4%

P(exactly 2R)= P(RRNNN)+P(RNRNN) +P(RNNRN) + P(RNNNR) +

P(NRRNN) + P(NRNRN) + P(NRNNR)

+ P(NNRRN)+P(NNRNR)

+P(NNNRR)

=10(13/23)(12/22)(11/21)(10/20)(9/19)

=10P(no R)

=about 38% chance