Two balls are randomly selected from a bowl containing 6 white balls and 5 black
ID: 3127190 • Letter: T
Question
Two balls are randomly selected from a bowl containing 6 white balls and 5 black balls. What is the probability that one of the drawn balls is white and the other black? A system consists of two components CI and C2. Let the probability that CI works without failure be 0.9 and the probability that C2 works without failure be 0.8. Find the probability that the system works without failure when (a) CI and C2 are connected in series (b) CI and C2 are connected in a parallel way. In the game of bridge, each of the four players gets 13 cards, if North and South have 8 spades between them, what is the probability of East has 3 spades and West has 2?Explanation / Answer
a)Bag contains 6 white and 5 Black balls.
Probality=No of desired draws from bag/total no of draws possible
Total no of draws possible=11C2
No of desired draws=5*6=30
Probabilty=30/11C2 =30/55 =0.545
b)When C1 and C2 are connected in series both should work properly for system to work without failure
Probabilty(series)=0.9*0.8= 0.72
When C1 and C2 are connected in parallel system will work fine unless both C1 and C2 fails.
Probabilty(series)= 1-0.1*0.2= 0.98
c)Remaining spades are 5 between East and West.
Total no of ways that we can divide 5spades among them is 25 =32
no of desired divisions = 5C3=10
Probablity =10/32 =0.3125