The probability that the marble is large or white is 0.5714.
<h3>What is probability?</h3>
Probability is the branch of mathematics that studies the possible outcomes of given events together with the outcomes' relative likelihoods and distributions.
Probability of an event is
P(A) = Number of favorable outcomes/ Total Number of outcomes
= n(A)/n(S)
where
P(A) is the probability of an event “A”
n(A) is the number of favorable outcomes
n(S) is the total number of events in the sample space.
We have,
Number of large marbles = 14
Number of small marbles = 10
Number of large green marbles = 8 which implies
Number of large white marbles = 14 - 8 = 6
Number of small white marbles = 4 which implies
Number of small green marbles = 10 - 4 = 6.
Now, let
Let X be the event of drawing large marble.
Let Y be the event of drawing small marble.
Let M be the event of drawing white marbles.
Let N be the event of drawing green marbles.
Since only one marble is drawn at a time ,
so P(X) = 14/24
P(Y) = 10/24
P(M) = 10/24
P(N) = 14/24
We have to find the probability that a marble is large or white i.e. P(X∪M).
P(X∪M) = P(X) + P(Y) - P(X∩M)
P(X∩M) = In 14 large marbles 6 are white marbles = 6/14.
P(X∪M) = P(X) + P(Y) - P(X∩M) = 14/24 + 10/24 - 6/14 = 0.5833+0.4167-0.4286 = 0.5714.
Therefore, the probability of drawing large or white marble is 0.5714.
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= 0