Question

In: Statistics and Probability

For a certain​ candy, 55​% of the pieces are​ yellow, 1515​% are​ red, 55​% are​ blue,...

For a certain​ candy,

55​%

of the pieces are​ yellow,

1515​%

are​ red,

55​%

are​ blue,

2020​%

are​ green, and the rest are brown.

​a) If you pick a piece at​ random, what is the probability that it is​ brown? it is yellow or​ blue? it is not​ green? it is​ striped?

​b) Assume you have an infinite supply of these candy pieces from which to draw. If you pick three pieces in a​ row, what is the probability that they are all​ brown? the third one is the first one that is​ red? none are​ yellow? at least one is​ green?

​a) The probability that it is brown is

nothing.

​(Round to three decimal places as​ needed.)The probability that it is yellow or blue is

nothing.

​(Round to three decimal places as​ needed.)The probability that it is not green is

nothing.

​(Round to three decimal places as​ needed.)The probability that it is striped is

nothing.

​(Round to three decimal places as​ needed.)​b) The probability of picking three brown candies is

nothing.

​(Round to three decimal places as​ needed.)

The probability of the third one being the first red one is

nothing.

​(Round to three decimal places as​ needed.)

The probability that none are yellow is

nothing.

​(Round to three decimal places as​ needed.)

The probability of at least one green candy is

nothing.

​(Round to three decimal places as​ needed.)

Solutions

Expert Solution

For a certain​ candy, 5​% of the pieces are​ yellow, 15​% are​ red, 5​% are​ blue, 20​% are​ green, and the rest are brown.

So here brown percentage = 100 - 5 - 15 - 5 - 20 = 55%

​a) If you pick a piece at​ random, what is the probability that it is​ brown? it is yellow or​ blue? it is not​ green? it is​ striped?

Answer :

Pr(It is brown) = 0.55

Pr(It is yellow or blue) = Pr(Yellow) + Pr(Blue) = 0.05 + 0.05 = 0.10

Pr(It is not green) = 1 - Pr(Green) = 1 - 0.20 = 0.80

Pr(It is striped) = 0.0

​b) Assume you have an infinite supply of these candy pieces from which to draw. If you pick three pieces in a​ row, what is the probability that they are all​ brown? the third one is the first one that is​ red? none are​ yellow? at least one is​ green?

Answer :

If we draw three pieces of these cany

Pr(THey are all brown) = Pr(First one is brown) * Pr(Second one is brown) * Pr(Third one is brown)

= 0.55 * 0.55 * 0.55 = 0.166

Pr(Third one is the first one that is red) = Pr(first one is red) * Pr(Third one is red) = 0.15 * 0.15 = 0.0225

Pr(None are yellow) = (1 - 0.05)3 = 1 - 0.953 = 0.143

probability of at least one green candy = Pr(At least one green candy) = 1 - Pr(No green candy) = 1 - (1 - 0.20)3 = 0.488

orchestra answered 2 years ago
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