4 8/10 points I Previous Answers A bag contains 22 colored blocks. 6 of them are

Question

4 8/10 points I Previous Answers A bag contains 22 colored blocks. 6 of them are red 5 of them are black, and 11 are green You randomly draw 3 blocks out of the bag. (a) What is the probability that all three blocks are green? (3/28) (b) What is the probability that 2 of them are red and one is black? (15308) (c) What is the probability that all 3 are the same color (all red or all black or all green)? (39/308) (d) What is the probability that the 3 blocks are each a different color? 14 (e) What is the probability that 2 blocks are one color and the other block is a different color? (2/308)

Explanation / Answer

Solution:

Given ,

number of red blocks = 6

number of black blocks = 5

number of green blocks= 11

3 blocks are drawn

total number of ways of drawing 3 blocks out of these 22 blocks = 22c3 = 1540

( e )

the number of ways that 2 blocks are one colour and the other block is different color = 6c2 * 16c1 + 5c2 *17c1 + 11c2 * 11c1

= 15 * 16 + 10 * 17 + 55 * 11

= 240 + 170 + 605

= 1015

the probability that 2 blocks are one colour and the other block is different color = 1015 / 1540

= 0.659

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