Probability Marbles
Probability is the chance of the outcome of an event of a particular experiment
. Probabilities are occurs always numbers between 0 (impossible) and 1(possible). The set of all possible outcomes of a particular experiment is called as sample space. For example probability of getting a^2 when rolling a dice is 1/6. In this lesson we will discuss about probability problems using marbles .
A probability is a way of expressing the knowledge with an event will occur. Statistics are a science which analysis, collecting the data surveys to designs the experiment. In this session, we have to learn some basics in probability and statistics. We have explained some concepts with examples in them. The following examples show the basics of them.
Probability is the likelihood of the occurrence of an event. The probability of event A is written P(A). Probabilities are always numbers between 0 (impossible) and 1 (possible), inclusive. Set of possible outcomes of a particular experiment is called as event. The set of all possible outcomes of an experiment is referred to as sample space. Fair coins has same probability of heads and tails. In this lesson we will discuss about probability problems using fair coin.
Example Problems
These solved problems will help you to understand how to solve the probability word problems.
Ex:1 In a box there are 30 marbles, 12 of which are red marbles, 9 are white marbles and 9 are black marbles. Find the probability of:
a) Red marble drawing first.
b) White marble drawing first.
c) Black marble drawing fourth if two red marble and one white marble had drawn.
Sol:
a) Let S = Sample space, n(S) = 30
A be the event of red marble drawing first, n(A) = 12
Probability of a red marble drawing first:
P(A) = (n(A))/(n(S)) = 12/30 = 2/5
b) Let B be the event of a white marble drawing first, n(B) = 9
Probability of a white marble drawing first:
P(B) = (n(B))/(n(S)) = 9/30 = 3/10
c) If two red marble and one white marble had drawn, then there would be 27 marbles remaining, 9 of which are black marbles. Let S1 be the sample space and C be the event of a black marble drawing.
n(S1) = 27
n(C) = 9
Probability of a black marble drawing after two red and one white marble has drawn
P(C) = (n(C))/(n(S1)) = 9/27 = 1/3 .
Ex:2 A box contains 8 orange marbles, 8 yellow marbles. If two marbles are drawn at random, find the probability that both are orange or yellow marbles.
Sol:
We have to select 2 marbles from 16 (8 + 8) marbles.
n(S) = 16C2 = (16!)/(2!X14!) = (16X15)/(2X1) = 240/2 = 120
Let A = Event of getting 2 orange marbles
B = Event of getting 2 yellow marbles
n(A) = 8C2 = (8!)/(2!X6!) = (8X7)/2 = 28
n(B) = 8C2 = (8!)/(2!X6!) = (8X7)/2 = 28
P(A) = (n(A))/(n(S)) = 28/120 = 7/30
P(B) = (n(B))/(n(S)) = 28/120 = 7/30
P(A or B) = P(A) + (B) = 7/30 + 7/30 = 7/15
P(A or B) = 7/15 .
Practice Problems
Solve these practice probability word problems.
Pr:1 In a box there are 25 marbles, 10 of which are white marbles, 15 are black marbles. Find the probability of:
a) Black marble drawing first.
b) White marble drawing after black.
Pr:2 A box contains 5 orange marbles, 7 yellow marbles. If two marbles are drawn at random, find the probability that 1 is yellow and 1 is orange marble.
Answer: 1) a) 3/5 , b) 5/12 2) 7/605
by: nitinp
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