Activities

Conditional probability - meaning

Conditional probability:

The probability of an event with a description that includes words such as "if" or "given that".

Example 1
 
Two dice are thrown

If the total is 10, what is the probability that a double occurs?

Find the value of P(double if total is 10).
 

The sample space when two dice are thrown contains 36 outcomes.

Because of the condition, the sample space is restricted to 3 outcomes, 1 of which is a double:

(4,6) (5,5) (6,4)
P(double if total is 10) = 1/3
2nd die
6
5
4
3
2
1
 
 
 
 
  
 
 
 
 
 
 
 
 
  
 
 
 
 
 
 
 
 
 
 
 
 
  
 
 
 
 
 
 
1
2
3
4
5
6
1st die


Example 2

If a double occurs, what is the probability that the total is 10?

Because of the condition, the sample space is restricted to 6 outcomes, 1 of which gives a total of 10:

(1,1) (2,2) (3,3) (4,4) (5,5) (6,6)
P(total of 10 if a double occurs) = 1/6
2nd die
6
5
4
3
2
1
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
  
 
 
 
 
 
1
2
3
4
5
6
1st die

Conditional probability - more two dice problems

Ball from bag - A ball is chosen at random from a bag containing fifteen red balls (numbered 1 to 15) and ten blue balls (numbered 16 to 25).  What is the probability that the ball is:
Coin flipped three times - A coin is tossed three times. What is the probability that:
  • the first toss is heads given that at least one toss is tails
  • at least one toss is tails given that the first toss is heads
  • exactly two tails are tossed given that the second toss is tails
  • the second toss is tails given that exactly two tails are tossed?

Card from pack - Two cards are dealt without replacement from a standard pack of 52 cards.  What is the probability that:

QMaths 12C - Ex 10.1 p 413 13e-i,15b-d,16