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An experiment has three possible outcomes, l, J, and K. The
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10 Dec 2020, 12:15
10 Dec 2020, 12:15
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An experiment has three possible outcomes, l, J, and K. The probabilities of the outcomes are 0.25, 0.35, and 0.40, respectively. If the experiment is to be performed twice and the successive outcomes are independent, what is the probability that K will not be an outcome either time?
(A) 0.36
(B) 0.40
(C) 0.60
(D) 0.64
(E) 0.80
Kudos for the right answer and explanation
(A) 0.36
(B) 0.40
(C) 0.60
(D) 0.64
(E) 0.80
Kudos for the right answer and explanation
Re: An experiment has three possible outcomes, l, J, and K. The
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11 Dec 2020, 13:29
11 Dec 2020, 13:29
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Solution:
The stem is stating there there are 3 possible outcomes, i, j, k with probabilities of outcome of .25, .35, and .40 respectively.
If the experiment is performed twice we are asked to find the probability that k WILL NOT be an outcome either time.
The simplest way to go about this is to negate the statement and find the probability of that since it'll be easier.
The negated statement is as follows: What is the probability that k WILL be an outcome either time?
Here are the following possibilities:
i,k -- .25*.40 = .1 (we multiply the probabilities given because we want I 'AND' K, (an 'and' statement in probability is a multiplication)
k,i -- .40*.25 = .1 (same as above)
j,k -- .35*.40 = .14
k,j -- .14 (same as above just flipped)
k,k -- .40*.40 = .16
Now that we have all the various routes to which a 'k' is achieved we add them all up because it can be i,k OR k,i OR j,k OR k,j OR k,k.
And using an 'or' is addition in probability
So now we get .1+.1+.14+.14+.16 = .640.
But remember that this is the negated statement and we actually want the probability of this not happening so simply perform the following operation:
1-.640 = .36 which is your final answer.
If this helped please leave kudos
The stem is stating there there are 3 possible outcomes, i, j, k with probabilities of outcome of .25, .35, and .40 respectively.
If the experiment is performed twice we are asked to find the probability that k WILL NOT be an outcome either time.
The simplest way to go about this is to negate the statement and find the probability of that since it'll be easier.
The negated statement is as follows: What is the probability that k WILL be an outcome either time?
Here are the following possibilities:
i,k -- .25*.40 = .1 (we multiply the probabilities given because we want I 'AND' K, (an 'and' statement in probability is a multiplication)
k,i -- .40*.25 = .1 (same as above)
j,k -- .35*.40 = .14
k,j -- .14 (same as above just flipped)
k,k -- .40*.40 = .16
Now that we have all the various routes to which a 'k' is achieved we add them all up because it can be i,k OR k,i OR j,k OR k,j OR k,k.
And using an 'or' is addition in probability
So now we get .1+.1+.14+.14+.16 = .640.
But remember that this is the negated statement and we actually want the probability of this not happening so simply perform the following operation:
1-.640 = .36 which is your final answer.
If this helped please leave kudos
General Discussion
Re: An experiment has three possible outcomes, l, J, and K. The
[#permalink]
18 Dec 2020, 07:38
18 Dec 2020, 07:38
5
Carcass wrote:
An experiment has three possible outcomes, l, J, and K. The probabilities of the outcomes are 0.25, 0.35, and 0.40, respectively. If the experiment is to be performed twice and the successive outcomes are independent, what is the probability that K will not be an outcome either time?
(A) 0.36
(B) 0.40
(C) 0.60
(D) 0.64
(E) 0.80
Kudos for the right answer and explanation
(A) 0.36
(B) 0.40
(C) 0.60
(D) 0.64
(E) 0.80
Kudos for the right answer and explanation
My reasoning - the prob(not K) is going to be 0.6 (1 - p(k) which is 0.4). Since we are looking at two successive outcomes, we can multiple the prob(not k) which calculates up to 0.36(0.6 * 0.6)
