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1 answer:
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Answer:
(a) Shown below.
(b) The probability that the first ball drawn is blue is 0.40.
(c) The probability that only white balls are drawn is 0.36.
Step-by-step explanation:
The balls in the urn are as follows:
Blue balls: B₁ and B₂
White balls: W₁, W₂ and W₃
It is provided that two balls are drawn from the urn, with replacement, and their color is recorded.
(a)
The possible outcomes of selecting two balls are as follows:
B₁B₁ B₂B₁ W₁B₁ W₂B₁ W₃B₁
B₁B₂ B₂B₂ W₁B₂ W₂B₂ W₃B₂
B₁W₁ B₂W₁ W₁W₁ W₂W₁ W₃W₁
B₁W₂ B₂W₂ W₁W₂ W₂W₂ W₃W₂
B₁W₃ B₂W₃ W₁W₃ W₂W₃ W₃W₃
There are a total of N = 25 possible outcomes.
(b)
The sample space for selecting a blue ball first is:
S = {B₁B₁, B₁B₂, B₁W₁, B₁W₂, B₁W₃, B₂B₁, B₂B₂, B₂W₁, B₂W₂, B₂W₃}
n (S) = 10
Compute the probability that the first ball drawn is blue as follows:
Thus, the probability that the first ball drawn is blue is 0.40.
(c)
The sample space for selecting only white balls is:
X = {W₁W₁, W₂W₁, W₃W₁, W₁W₂, W₂W₂, W₃W₂, W₁W₃, W₂W₃, W₃W₃}
n (X) = 9
Compute the probability that only white balls are drawn as follows:
Thus, the probability that only white balls are drawn is 0.36.
Complete Question
The complete question is shown on the first uploaded image
Answer:
a
The probability that he or she would choose the pair of socks in the center position is
The correct answer choice is
X has a binomial distribution with parameters n=100 and p=1/5
b
The mean is
The standard deviation is
c
The probability,
d
The correct answer is
The experiment supports the center stage effect. If participants were truly picking the socks at random, it would be highly unlikely for 34 or more to choose the center pair.
Using the R the probability
The probabilities
Step-by-step explanation:
Since the person selects his or her desired pair of socks at random , then the probability that the person would choose the pair of socks in the center position from all the five identical pair is mathematically evaluated as
The mean of this distribution is mathematical represented as
substituting the value
The standard deviation is mathematically represented as
substituting the value
Applying normal approximation the probability that 34 or more subjects would choose the item in the center if each subject were selecting his or her preferred pair of socks at random would be mathematically represented as
By standardizing the normal approximation we have that
Now z is mathematically evaluated as
Substituting values
So using the z table the is 0.0002
The probability P and Pe that 34 or more subject would choose the center pair is very small So
The correct answer is
The experiment supports the center stage effect. If participants were truly picking the socks at random, it would be highly unlikely for 34 or more to choose the center pair.
Angles RLN and MLK would be vertical angles.
Right. Vertical angles are formed when their sides share the same lines. RL shares the same line with LM and NL shares the same line with LK (see the attached diagram), so that means both angles form a vertical pair.
Angles RLN and MLN would be vertical angles.
Wrong. They are linear pairs, because they are adjacent and supplementary. Adjacent angles share a side – in this case, LN. Supplementary angles sum 180°, which you can see is right because the other sides (ML and RL) are in the same line. RLN and MLN sum the same as the size of RLM, which is a line, so it’s 180°. <span>
Angles RLN and KLM would be a linear pair. </span>
Wrong. They would be a vertical pair (see definition of vertical pair in the first option). RL is opposed to LM and LN is opposed to KL.
Angles RLN and KLN would be a linear pair.
Wrong. KLN is actually a line, so it’s actually 180°, so it can’t be a linear pair with KLN. Linear pairs sum 180°, which is impossible because KLN itself is already 180°, so any sum will throw a higher number.
Right. Vertical angles are formed when their sides share the same lines. RL shares the same line with LM and NL shares the same line with LK (see the attached diagram), so that means both angles form a vertical pair.
Angles RLN and MLN would be vertical angles.
Wrong. They are linear pairs, because they are adjacent and supplementary. Adjacent angles share a side – in this case, LN. Supplementary angles sum 180°, which you can see is right because the other sides (ML and RL) are in the same line. RLN and MLN sum the same as the size of RLM, which is a line, so it’s 180°. <span>
Angles RLN and KLM would be a linear pair. </span>
Wrong. They would be a vertical pair (see definition of vertical pair in the first option). RL is opposed to LM and LN is opposed to KL.
Angles RLN and KLN would be a linear pair.
Wrong. KLN is actually a line, so it’s actually 180°, so it can’t be a linear pair with KLN. Linear pairs sum 180°, which is impossible because KLN itself is already 180°, so any sum will throw a higher number.