Introduction to compound events:
Numerical measure of the likelyhood of an event to occur. If in an experiment there are n possible ways exhaustive and mutually exclusive and out og them in m ways int he A occurs . then the probability of occurrence of the event A is given by ,
P(A) = m / n
Compound Events:
An experiment consists of two or more simple events called as compound events.
Examples:
Rolling a die
Tossing two dice and two coins
Types of Compound Events :
There are two types in compound events ,
Independent compound Event
Dependent compound Event
Independent Event :
In compound events, when the outcome of one event does not change the outcome of the second event, these are called independent events.
The probability of two independent events is obtained by multiplying the probability of the first event by the probability of the second event.
Formula:
The probability of compound events when they are Independent Event is,
P (A and B) = P (A) . P (B) [A and B are two events]
Dependent Event:
Dependent events are two or more events where the outcome of one does affect the outcome of the other.
If 2 events, u and v are mutually exclusive, then the probability that either U or V occurs is the sum of the probability of u and probability of v.
Formula :
P(u or v) = P(u) + P(v)
I am planning to write more post on Tree Diagram Template, Sample Space Probability. Keep checking my blog.
Example Problems for Compound Events
Example compound events problem 1:
Jack is going to a stationary shop to buy stationary items. There are 20 ball point pens, 35 gel pens and 15 parker pens. Jack randomly chosen one pen. What’s the probability that john picked one is ball point or gel?
Solution:
Total no .of pens = 20 + 35+15 = 70
Since a pen cannot be both ball point and a gel, the events are mutually exclusive. Hence,
P (ball point or gel) = (no. of ball point pens + no. of gel pens) / Total no. of pens
= (20 + 35) / 70
= 11/ 14.
Answer:
The final answer is (11 / 14)
Example compound events problem 2:
There are three black cats and four grey cats in a cage, and none of them want to be in there. The cage door opens briefly and two cats escape. What is the probability that both escaped cats are black?
Solution:
Total number of cats = 3 black cats + 4 grey cats = 7
Probability of first cat escaped is black = 3 / 7
P (next one also black) = 2 / 6
Probability of both escaped cats is black:
= 3 / 7 * 2 / 6
= 6 / 42 = 1 / 7
This is an example for dependent event .
Numerical measure of the likelyhood of an event to occur. If in an experiment there are n possible ways exhaustive and mutually exclusive and out og them in m ways int he A occurs . then the probability of occurrence of the event A is given by ,
P(A) = m / n
Compound Events:
An experiment consists of two or more simple events called as compound events.
Examples:
Rolling a die
Tossing two dice and two coins
Types of Compound Events :
There are two types in compound events ,
Independent compound Event
Dependent compound Event
Independent Event :
In compound events, when the outcome of one event does not change the outcome of the second event, these are called independent events.
The probability of two independent events is obtained by multiplying the probability of the first event by the probability of the second event.
Formula:
The probability of compound events when they are Independent Event is,
P (A and B) = P (A) . P (B) [A and B are two events]
Dependent Event:
Dependent events are two or more events where the outcome of one does affect the outcome of the other.
If 2 events, u and v are mutually exclusive, then the probability that either U or V occurs is the sum of the probability of u and probability of v.
Formula :
P(u or v) = P(u) + P(v)
I am planning to write more post on Tree Diagram Template, Sample Space Probability. Keep checking my blog.
Example Problems for Compound Events
Example compound events problem 1:
Jack is going to a stationary shop to buy stationary items. There are 20 ball point pens, 35 gel pens and 15 parker pens. Jack randomly chosen one pen. What’s the probability that john picked one is ball point or gel?
Solution:
Total no .of pens = 20 + 35+15 = 70
Since a pen cannot be both ball point and a gel, the events are mutually exclusive. Hence,
P (ball point or gel) = (no. of ball point pens + no. of gel pens) / Total no. of pens
= (20 + 35) / 70
= 11/ 14.
Answer:
The final answer is (11 / 14)
Example compound events problem 2:
There are three black cats and four grey cats in a cage, and none of them want to be in there. The cage door opens briefly and two cats escape. What is the probability that both escaped cats are black?
Solution:
Total number of cats = 3 black cats + 4 grey cats = 7
Probability of first cat escaped is black = 3 / 7
P (next one also black) = 2 / 6
Probability of both escaped cats is black:
= 3 / 7 * 2 / 6
= 6 / 42 = 1 / 7
This is an example for dependent event .
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