Answered

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Samira and Sonia each have a bag containing 20 sweets. In each bag, there are 5 red, 6 green and 9 yellow sweets.
(a)
(b)
Samira chooses one sweet at random from her bag.
Write down the probability that she chooses a yellow sweet.
[1] Sonia chooses two sweets at random, without replacement, from her bag.
(i) Show that the probability that she chooses two green sweets is 3 . 38
(ii) Calculate the probability that the sweets she chooses are not both the same colour.

Sagot :

reinhard10158

Step-by-step explanation:

there must be some typos here. but I try to address the right issues.

there is nothing under (a). so, really nothing to answer.

(b)

there are 20 sweets in her bag. 9 if the 20 are yellow.

so, the probability is the ratio of desired possibilities vs. total possibilities.

that is, tada! 9/20

that is the probabilty for Samira to pick a yellow sweet.

[1] (i)

again, 20 sweets to start with.

6 are green.

when she picks the first one, her probability to pick a green one is 6/20 = 3/10 = 0.3

and now, under the assumption that this came true, she picks another sweet.

this time she had only 19 left, and 5 of them are green.

so, this probabilty is 5/19

now both events need to happen for the case we are discussing. there is no overlapping, no ors, ifs and buts. it is just the product of both probabilities.

3/10 × 5/19 = 15/190 = 3/38

I think that is what the description asks for.

(ii)

that probability is

first selection is red and second is not red +

first selection is green and second is not green +

first selection is yellow and second is not yellow

so,

red and not red

5/20 = 1/4 red

15/19 not red (there are still 15 sweets of other colors in the bag, but again now only 19 total).

red and not red = 1/4 × 15/19 = 15/76 = 0.1974

green and not green

6/20 = 3/10 = green

14/19 = not green

green and not green = 3/10 × 14/19 = 52/190 = 26/95 =

= 0.2737

yellow and not yellow

9/20 = yellow

11/19 = not yellow

yellow and not yellow = 9/20 × 11/19 = 99/380 = 0.2606

so, now assuming up all 3 possibilities ("or" = sum) gives us the general possibility of selecting two different colors

= 0.7316

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