Abag contains 11red beads 4 green beads 1 purple bead. Two beads are drawn without replacement in the bag. A). Calculate probability ttwo beads are same colour. And. B) calculate probability purple bead is not taken.
You'll get better results if you follow directions and put the SCHOOL SUBJECT in that box, not the name of your school.
a) could be either RR or GG
prob(RR = (11/16)(10/15) = 11/24
prob(GG) = (4/16)(3/15) = 9/20
prob(2 same colour) = 11/24 + 9/20 = 109/120
prob (one purple , one none) = (1/16)(15/15) + 15/16)(1/15) = 1/8
prob(NOT a purple) = 1 - 1/8 = 7/8
7/8
To calculate the probabilities, we need to determine the total number of possible outcomes and the number of favorable outcomes.
First, let's determine the total number of beads in the bag:
Total number of beads = 11 red beads + 4 green beads + 1 purple bead = 16 beads
A) To calculate the probability that two beads drawn are the same color, we need to consider two cases separately:
Case 1: Drawing two red beads
Number of favorable outcomes = 11C2 (combination of choosing 2 from 11 red beads)
Number of total outcomes = 16C2 (combination of choosing 2 from 16 beads)
Case 2: Drawing two green beads
Number of favorable outcomes = 4C2 (combination of choosing 2 from 4 green beads)
Number of total outcomes = 16C2 (combination of choosing 2 from 16 beads)
Now, we can calculate the probability for each case and add them together:
P(two beads are the same color) = (Number of favorable outcomes for case 1 + Number of favorable outcomes for case 2) / Number of total outcomes
B) To calculate the probability that a purple bead is not taken, we need to consider the case of not drawing the purple bead:
Number of favorable outcomes = 15C2 (combination of choosing 2 from the 15 non-purple beads, i.e., red and green beads)
Number of total outcomes = 16C2 (combination of choosing 2 from the 16 beads)
Now, we can calculate the probability:
P(purple bead is not taken) = Number of favorable outcomes / Number of total outcomes
To find the exact values of these probabilities, we need to calculate the combinations and divide them accordingly.