Answer: [tex]\dfrac15[/tex]
Step-by-step explanation:
Given : A cloth bag contains 6 cards numbered 1 through 6. Two cards are drawn without replacement.
Favorable outcome: sum of the numbers on the two drawn cards is 7
Since 1+6 = 7 , 2+5=7, 4+3 = 7
So, sum of 7 can be obtained as (1, 6), (2, 5), (3, 4), (4, 3), (5, 2) and (6, 1)
Probability of getting (first 1, second 6) = [tex]\dfrac16\times\dfrac15=\dfrac{1}{30}[/tex]
Probability of getting (first 2, second 5) = ([tex]\dfrac16\times\dfrac15=\dfrac{1}{30}[/tex]
Probability of getting (first 3, second 4) =[tex]\dfrac16\times\dfrac15=\dfrac{1}{30}[/tex]
Probability of getting (first 4, second 3) = [tex]\dfrac16\times\dfrac15=\dfrac{1}{30}[/tex]
Probability of getting (first 5, second 2) = [tex]\dfrac16\times\dfrac15=\dfrac{1}{30}[/tex]
Probability of getting (first 6, second 1) =[tex]\dfrac16\times\dfrac15=\dfrac{1}{30}[/tex]
Required probability =[tex]6\times\dfrac{1}{30}=\dfrac15[/tex]
Hence, the required probability = [tex]\dfrac15[/tex]
