1 Answer

Aaron Maenpaa · Answer 1 · 2019-04-20T09:36:31+0000

A bag of 25 tulip bulbs contains:

Use theoretical definition of probability:

$Pr=\frac{\text{number of favorable outcomes}}{\text{number of possible outcomes}}.$

1. What is the probability that two randomly selected tulip bulbs are both red?

The number of favorable outcomes is the number of ways to select 2 red bulbs from 10 red bulbs:

$C_(10)^2=(10!)/(2!(10-2)!)=(10!)/(2!\cdot 8!)=(8!\cdot 9\cdot 10)/(2\cdot 8!)=(9\cdot 10)/(2)=45.$

The number of possible outcomes is the number of ways to select 2 bulbs from 25 bulbs:

$C_(25)^2=(25!)/(2!(25-2)!)=(25!)/(2!\cdot 23!)=(23!\cdot 24\cdot 25)/(2\cdot 23!)=(24\cdot 25)/(2)=300.$

Then

$Pr(\text{2 red})=(45)/(300)=(15)/(100)=0.15.$

2. What is the probability that the first bulb selected is red and the second yellow?

The probability to select 1st bulb red is
(10)/(25), the probability to select second bulb yellow is
(8)/(24) (only 24 bulbs left).

Then use the product rule:

$Pr(\text{1st red, 2nd yellow})=(10)/(25)\cdot (8)/(24)=(2)/(5)\cdot (1)/(3)=(2)/(15).$

3. What is the probability that the first bulb selected is yellow and the second red?

The probability to select 1st bulb yellow is
(8)/(25), the probability to select second bulb red is
(10)/(24) .

Then use the product rule:

$Pr(\text{1st yellow, 2nd red})=(8)/(25)\cdot (10)/(24)=(8)/(25)\cdot (5)/(12)=(40)/(300)=(2)/(15).$

4. What is the probability that one bulb is red and the other yellow?

Two cases are possible: 1st-red, 2nd - yellow or 1st - yellow, 2nd - red. Then use the addition rule:

$Pr(\text{one yellow, another red})=(2)/(15)+ (2)/(15)=(4)/(15).$

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