Question

A bag of 29 tulip bulbs contains 11 red tulip​ bulbs, 12 yellow tulip​ bulbs, and 6 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?

Answer 1

Ans(a)

We have a bag of total 29 tulip bulbs, out of which 11(red tulip bulb), 12(yellow tulip bulb), 6(purple tulip bulb).

Since there are 29 bulbs in the bag out of which 2 bulbs can be drawn in ways.

So, the total number of elementary events =

Also there are 11 red tulip bulbs out of which 2 can be drawn in ways.

Favourable number of elementary events =

So, the required probability of selecting both red tulip bulbs is=

(b) Consider a the two events :

A= drawing Red bulb in first draw, B=drawing the Yellow bulb in second draw.

The probability of drawing the first red bulb and the second yellow is given as:

Now,

After drawing the one red bulb in first draw, total 28 bulbs are left in the bag, out of which 12 are yellow tulip bulbs.

The probability of drawing the second bulb yellow given that the first drawn bulb is red given as:

Hence, the required probability that the first drawn bulb is red and the second is yellow is given as:

(c)

Consider a the two events :

A= drawing Yellow bulb in first draw, B=drawing the Red bulb in second draw.

The probability of drawing the first Yellow bulb and the second Red is given as:

Now, after drawing the one Yellow bulb in first draw, total 28 bulbs are left in the bag, out of which 11 are Red tulip bulbs.

The probability of drawing the second bulb Red given that the first drawn bulb is Yellow given as:

Hence, the required probability that the first drawn bulb is Yellow and the second is Red is given as:

(d) Out of 29 tulip bulbs in a bag 2 bulb can be selected in ways.

Total number of elementary events=

There are 11 red tulip bulbs and 12 yellow tulip bulbs out of which 2 bulbs bulbs can be selected in ways.

So, the favourable number of elementary events=

Hence, the required probability(one bulb is Red and the other is Yellow) =