Introduction to solving possibility problem
Probability or possibility determines the possible outcomes of a certain an experiment. One or more possible outcome of an experiment is referred to as event. For instance, when tossing a coin head and tail are the two possible outcomes. In independent event one event does not affect the other event. In dependent event one event does affect the other event. Two events are cannot happen at the same time, they are called mutually exclusive events.
Solving Possibility Problem - Examples
Solving Problem 1: 4 balls are drawn with replacement from a bag containing 20 blue and 16 orange balls.
Find the possibility of a) both the balls are orange b) first ball is blue and second ball orange c) One is blue and the other is orange.
Solution:
Total = 20 blue + 16 orange = 36. From that 4 balls are drawn.
Let’s A: Orange ball and B: Blue ball
P(A) = 16/36 = 4/9 and P(B) = 20/36 = 5/9
a) Both are orange
P( orange and orange) = P( A n A) = P(A) · P(A)
= 4/9 · 4/9 = 16/81
b) First ball is blue and second is orange.
P( orange n blue) = P( A) · P( B) = 4/9 · 5/9 = 20/81
c) one is blue and the other is orange
= P(A) · P(B) + P(B) · P(A)
= 4/9 · 5/9 + 5/9 · 4/9
= 20/81 + 20/81 = 40/81.
Solving Problem 2: A box contains 6 apples and 6 oranges. A fruit is drawn at random; fruit is noted and is returned to the box. Moreover, 2 additional fruits of the same verity are put in the box and then a fruit is drawn. What is the possibility that the second fruit is apple?
Solution:
Case 1: Let us draw an apple first.
S1 = 6 apple + 6 orange = 12
A1 : drawing an apple, P(A1 ) = 6/12 = 1/2
Now after adding 2 more apples
S2 = 8 apple + 6 orange = 14
A2 : drawing an apple, P(A2) = 8/14 = 4/7
P(an apple and an apple) = 1/2 · 4/7 = 4/14 = 2/7
Case 2: Let us draw an orange first
S1 = 6 apple + 6 orange = 12
A1 : Drawing an orange, P(A1) = 6/12 = 1/2
Now after adding 2 more oranges
S2 = 6 apple + 8 orange = 14
A2 : Drawing an apple, P(A2) = 6/14 = 3/7
P(an orange and an apple)= 1/2 * 3/7 = 3/14
P(in both the cases) = 2/7 + 3/14 = 49/98 = 1/ 2 Ans.
Solving Possibility Problem - Practice
Solving Problem 1: Two dice are rolled; find the probability that the total is a) equal to 3 b) equal to 6 c) greater than 10
Answer: a) 1/18 b) 5/36 c) 1/12
Solving Problem 2: Find the probability of getting king from deck of card?
Answer: 1/13
Probability or possibility determines the possible outcomes of a certain an experiment. One or more possible outcome of an experiment is referred to as event. For instance, when tossing a coin head and tail are the two possible outcomes. In independent event one event does not affect the other event. In dependent event one event does affect the other event. Two events are cannot happen at the same time, they are called mutually exclusive events.
Solving Possibility Problem - Examples
Solving Problem 1: 4 balls are drawn with replacement from a bag containing 20 blue and 16 orange balls.
Find the possibility of a) both the balls are orange b) first ball is blue and second ball orange c) One is blue and the other is orange.
Solution:
Total = 20 blue + 16 orange = 36. From that 4 balls are drawn.
Let’s A: Orange ball and B: Blue ball
P(A) = 16/36 = 4/9 and P(B) = 20/36 = 5/9
a) Both are orange
P( orange and orange) = P( A n A) = P(A) · P(A)
= 4/9 · 4/9 = 16/81
b) First ball is blue and second is orange.
P( orange n blue) = P( A) · P( B) = 4/9 · 5/9 = 20/81
c) one is blue and the other is orange
= P(A) · P(B) + P(B) · P(A)
= 4/9 · 5/9 + 5/9 · 4/9
= 20/81 + 20/81 = 40/81.
Solving Problem 2: A box contains 6 apples and 6 oranges. A fruit is drawn at random; fruit is noted and is returned to the box. Moreover, 2 additional fruits of the same verity are put in the box and then a fruit is drawn. What is the possibility that the second fruit is apple?
Solution:
Case 1: Let us draw an apple first.
S1 = 6 apple + 6 orange = 12
A1 : drawing an apple, P(A1 ) = 6/12 = 1/2
Now after adding 2 more apples
S2 = 8 apple + 6 orange = 14
A2 : drawing an apple, P(A2) = 8/14 = 4/7
P(an apple and an apple) = 1/2 · 4/7 = 4/14 = 2/7
Case 2: Let us draw an orange first
S1 = 6 apple + 6 orange = 12
A1 : Drawing an orange, P(A1) = 6/12 = 1/2
Now after adding 2 more oranges
S2 = 6 apple + 8 orange = 14
A2 : Drawing an apple, P(A2) = 6/14 = 3/7
P(an orange and an apple)= 1/2 * 3/7 = 3/14
P(in both the cases) = 2/7 + 3/14 = 49/98 = 1/ 2 Ans.
Solving Possibility Problem - Practice
Solving Problem 1: Two dice are rolled; find the probability that the total is a) equal to 3 b) equal to 6 c) greater than 10
Answer: a) 1/18 b) 5/36 c) 1/12
Solving Problem 2: Find the probability of getting king from deck of card?
Answer: 1/13
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