Question

A bag contains 6 red marbles, 10 white marbles, and 7 blue marbles. You draw 4 marbles out at random, without replacement. What is the probability that all the marbles are red

Answer 1

Answer:

3/1771

Step-by-step explanation:

Probability is the chance or likelihood that an event will occur.

Probability = expected outcome/total outcome

Total outcome = total number of marbles

Total outcome = 6+7+10 = 23marbles

If four marbles are drawn, the probability that they are all red is expressed as;

Pr(picking the first red marble) = 6/23

Since it is without replacement, the total marble becomes 22

Pr(picking the second) = 5/22

Pr(picking the third marbles = 4/21

Pr(picking the 4th marble) = 3/20

Note that the number of red marbles keep reducing and the total marble keep reducing as well.

Pr(picking the 4marbles) = 6/23×5/22×4/21×3/20 (we multiplied because or is an independent events)

Pr(picking the 4marbles) = 360/212520

Pr(picking 4 red marbles) = 72/42504 =36/21,252

= 9/5313

= 3/1771

Hence the probability of picking 4 marbles at random without replacement is 3/1771