There are 5 marbles in a bag - 2 are orange and 3 are blue.
There are 5 marbles in a bag - 2 are orange and 3 are blue. If two marbles are pulled from the bag, what is the probability Y that at least one will be orange?
Answer/Solution
Y=7/10
Steps/Work
Method 1
Probability that at least one out of two marbles will be orange = 1 - Probability that both marbles are blue = 1- P(First marble is blue) * P (Second Marble is Blue) = 1- (3/5)(2/4) = 7/10
Method 2
Probability that at least one marble will be orange = P( First Marble is Orange)*P(Second Marble is Blue) + P (First Marble is Blue)*P(Second Marble is Orange) + P(First Marble is Orange) *P(Second Marble is Orange) = (2/5)*(3/4)*2 + (2/5)*(1/4) = 7/10
Method 3
Probabilty that at least one marble will be orange = 1 - Probability that both marbles are blue
= 1 - (Number of ways 2 blue marbles out of 3 can be pulled)/(Number of ways 2 marbles out of 5 can be pulled)
= 1 - 3C2/5C2
= 1-(3/10) = 7/10
Answer :A
Probability that at least one out of two marbles will be orange = 1 - Probability that both marbles are blue = 1- P(First marble is blue) * P (Second Marble is Blue) = 1- (3/5)(2/4) = 7/10
Method 2
Probability that at least one marble will be orange = P( First Marble is Orange)*P(Second Marble is Blue) + P (First Marble is Blue)*P(Second Marble is Orange) + P(First Marble is Orange) *P(Second Marble is Orange) = (2/5)*(3/4)*2 + (2/5)*(1/4) = 7/10
Method 3
Probabilty that at least one marble will be orange = 1 - Probability that both marbles are blue
= 1 - (Number of ways 2 blue marbles out of 3 can be pulled)/(Number of ways 2 marbles out of 5 can be pulled)
= 1 - 3C2/5C2
= 1-(3/10) = 7/10
Answer :A