From a bag of M&Ms consisting of 3 green, 4 red, 4 yellow, and 3 blue you randomly select 4 M&Ms. Find the probability that when you open your hand, you find only yellow or blue colors. Give your answer to three significant decimal places.

0.399%

Step-by-step explanation:

Step 1: The total M&Ms in the bag is: 3 green, 4 red, 4 yellow, and 3 blue

= 3 + 4 + 4 +3 = 12

Step 2: When we select 4 M&Ms, The total number of random sample spaces are : 14C4 = 1001 (please use casio fx570 ES)

In other to have only yellow or blue colors, it means we have 2 cases:

- Only yellow when we pick 4, so the result is: 1 (4 yellows)

- Only blue when we pick 4, so the result is:  3 (3 blues + 1 green) ,  (3 blues + 1 red) +  (3 blues + 1 yellow)

Step 3: Take the total number of results divided by the total number of sample spaces, we have: (1+3) /1001*100% = 0.399%

34.5 cm

step-by-step explanation:

generally for a circular segment of angle, θ° and radius r

arc length

= (θ/360) x circumference

= (θ/360) x 2πr

in our case, θ = 60°, π=3.142 and r = 33 cm

substitute into above formula

arc length

= (60/360) x 2(3.142)( 33) = 34.5 cm