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shutvik [7]
3 years ago
6

You have a bag full of apples. There are 12 Jonathan (red), 6 Granny Smith (green), and 3 Golden Delicious (yellow) apples in th

e bag. The apples are all of similar size and shape. You reach into the bag (without looking) and pull out the number of apples listed in each scenario below.
a. Select 3 apples with replacement. Find the probability that all three are green.
b. Select 3 apples with replacement. Find the probability that none are red.
C. Select 4 apples without replacement. Find the probability that you get at LEAST 2 red apples.
d. Select 2 apples without replacement. Find the probability that the second apple is yellow given that the first apple is red.
Mathematics
2 answers:
scoray [572]3 years ago
8 0

Answer:

a) 0.032

b) 0.063

c) 0.313

d) 0.086

Step-by-step explanation:

12 red apples, 6 green apples and 3 yellow.

We have 21 apples!

a) the probability is

\frac{\frac{6!}{3!(6-3)!}}{\frac{21!}{3!(21-3)!}}=\frac{6!3!18!}{3!3!21!}=0.032

(all combnation to select tree green apples of 6 green apples derived with number of combinations to select 3 apples from all 21 apples)

b) probability of none are red is probability of chose 3 apples of 9 (sum of green and yellow).

\frac{{9\choose 3}}{21\choose 3}=0.063

c) least 2 red apples mean it will be 2 red, or 3 red or 4 red, so it is a sum of these tree probabilities.

\frac{{12 \choose 2}}{{21 \choose 2}}*\frac{{9\choose 2}}{{19\choose 2}}+\frac{{12 \choose 3}}{{21 \choose 3}}*\frac{{9\choose 1}}{{18\choose 1}}+\frac{{12 \choose 4}}{{21 \choose 4}}

=0.15+0.08+0.083=0.313

* expl: we have product because to chose 2 red apples has a probability and to chose 2 not red apples has a probabilit \frac{{9\choose 2}}{{19\choose 2}}  (9 sum of not red apples and 19 is 21 - chosen 2 red apples) *

d) It isa product of probability that you chose 1 red apple of 21 apples, and to chose 1 yellow apple of 20 apples

\frac{{12\choose 1}}{{21\choose 1}}*\frac{{3\choose 1}}{{20\choose 1}}=0.086

tensa zangetsu [6.8K]3 years ago
5 0

Answer:

The total number of apples is 17

Step-by-step explanation:

(a)

Number of green apples = 4

P ( that all three apples are green)

= (limit 4 and 3) / (limit 17 and 3)

= 4! / 3!(4−3)!

= 17! / 3!(17−3)!

= 1 / 170

= 0.005

(b)

Number of red apples = 8

P(that all three apple are green)

=(limit 8 and 3) / (limit 17 and 3)

= 8! / 3!(8−3)!

= 17! / 3!(17−3)!

= 7 / 85

= 0.082

Now,

P(that no three apple is red)= 1−0.082 = 0.918

c)

P(of selecting 4 apple that contain at least 2 red apples)

= (limit 8 and 2) /( limit 17 and 2) X (2/15) + (limit 8 and 3) /(limit 17 / 3) X (1/14)

= (7/34) × (2/15) + (7/85) × (1/14)

= 0.027 + 0.058

= 0.085

d)

P(that the second apple selected is yellow given that the first apple is red)

= (limit 5 and 1) / ( limit 16 and 1)

= 5! / 1!(5−1)!

= 16! / 1!(16−1)!

= 5 /16

= 0.3125

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