Suppose an opaque jar contains 3 red marbles and 10 green marbles. The following exercise refers...

Suppose an opaque jar contains 3 red marbles and 10 green marbles. The following exercise refers to the experiment of picking two marbles from the jar without replacing the first one. What is the probability of getting a green marble first and a red marble second?

Expert Solution

Suppose an opaque jar contains 3 red marbles and 10 green marbles.
the experiment of picking two marbles from the jar without replacing the first one.

the probability of getting a green marble first and a red marble second

using probability formulas,
probability = number of favorable events/total number of events
ncr = n!/(n-r)!*r!
now,
probability of getting a green marble first = 10c1/13c1
10c1 = 10!/(10-1)!*1!
10c1 =10*9!/(9!)*1
10c1 = 10 similarly, 13c1 = 13
probability of getting a green marble first = 10c1/13c1 = 10/13
probability of getting a red marble second = 3c1 /12c1 = 3/12
probability of getting a red marble second = 1/4
the probability of getting a green marble first and a red marble second = (10/13 )*(1/4)
the probability of getting a green marble first and a red marble second = 5/26 = 0.1923

Answer:
the probability of getting a green marble first and a red marble second = 5/26 = 0.1923

orchestra answered 1 year ago

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