A bag of 29 tulip bulbs contains 10 red tulip bulbs, 10 yellow tulip bulbs, and 9 purple tulip bulbs. (a) What is the probability that two randomly selected tulip bulbs are both red? (b) What is the probability that the first bulb selected is red and the second yellow? (c) What is the probability that the first bulb selected is yellow and the second red? (d) What is the probability that one bulb is red and the other yellow?
Accepted Solution
A:
Answer:a.The probability that two randomly selected tulip bulbs both are red=[tex]\frac{45}{406}[/tex].b.The probability that the first bulb selected is red and second yellow=[tex]\frac{50}{406}[/tex].c.The probability that the first bulb selected is yellow and the second red=[tex]\frac{50}{406}[/tex].d.The probability that one bulb is red and other yellow=[tex]\frac{50}{203}[/tex].Step-by-step explanation:Given Total number of bulbs= 29Number of bulbs of red=10Number of yellow bulbs=10Number of purple bulbs=9Formula of probability, P(E)=[tex]\frac{favourable \; cases}{total\;number\; of \; cases}[/tex]a.The probability that two randomly selected tulip bulbs are both red=[tex]\frac{10}{29}\times\frac{9}{28}=\frac{45}{406}[/tex].b.The probability of getting first bulb is red=[tex]\frac{10}{29}[/tex].The probability of getting second bulb is yellow=[tex]\frac{10}{28}[/tex]Hence,the probability that the firs bulb selected is red and the second bulb yellow=[tex]\frac{10}{29}\times\frac{9}{28}=\frac{45}{406}[/tex]c. The probability of getting firs bulb is yellow =[tex]\frac{10}{29}[/tex]The probability of getting second bulb is red=[tex]\frac{10}{28}[/tex]Hence,the probability that the firs bulb selected is yellow and the second bulb red=[tex]\frac{10}{29}\times\frac{10}{28}=\frac{50}{406}[/tex].d.The probability of getting first bulb is red and second is yellow=[tex]\frac{50}{406}[/tex]The probability of getting first bulb is yellow and second is red=[tex]\frac{50}{406}[/tex] The probability that one bulbe is red and other is yellow= probability of getting first bulb is red and other yellow+ probability of getting first bulb is yellow and other is redHence, the probability of getting one bulb is red and other is yellow=[tex]\frac{50}{406}+\frac{50}{406}=\frac{50}{203}[/tex]