Question

A bag of 34 tulip bulbs contains 13 red tulip​ bulbs, 11 yellow tulip​ bulbs, and 10 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

(a)

Selection 1: Red tulip bulb

Red tulip bulb = 13

Yellow tulip bulb = 11

Purple tulip bulb = 10

Total tulip bulbs = 34

So,

P(Selection 1: Red tulip bulb) = 13/34 = 0.3824

Selection 2: Red tulip bulb

Red tulip bulb = 12

Yellow tulip bulb = 11

Purple tulip bulb = 10

Total tulip bulbs = 33

So,

P(Selection 2: Red tulip bulb) = 12/33 = 0.3636

So,

P(Both Red) = 0.3824 X 0.3636 = 0.1391

So,

Answer is:0.1391

(b)

Selection 1: Red tulip bulb

Red tulip bulb = 13

Yellow tulip bulb = 11

Purple tulip bulb = 10

Total tulip bulbs = 34

So,

P(Selection 1: Red tulip bulb) = 13/34 = 0.3824

Selection 2: Yellow tulip bulb

Red tulip bulb = 12

Yellow tulip bulb = 11

Purple tulip bulb = 10

Total tulip bulbs = 33

So,

P(Selection 2: Yellow tulip bulb) = 11/33 = 0.3333

So,

P(First Red& Second Yellow) = 0.3824 X 0.3333 = 0.1275

So,

Answer is:0.1275

(c)

Selection 1: Yellow tulip bulb

Red tulip bulb = 13

Yellow tulip bulb = 11

Purple tulip bulb = 10

Total tulip bulbs = 34

So,

P(Selection 1: Yellow tulip bulb) = 11/34 = 0.3235

Selection 2: Red tulip bulb

Red tulip bulb = 13

Yellow tulip bulb = 10

Purple tulip bulb = 10

Total tulip bulbs = 33

So,

P(Selection 2: Red tulip bulb) = 13/33 = 0.3939

So,

P(First Yellow & Second Red) = 0.3235 X 0.3939 = 0.1274

So,

Answer is:0.1274

(d)

Case 1: Selection 1: Red & Selection 2: Yellow:

Selection 1: Red tulip bulb

Red tulip bulb = 13

Yellow tulip bulb = 11

Purple tulip bulb = 10

Total tulip bulbs = 34

So,

P(Selection 1: Red tulip bulb) = 13/34 = 0.3824

Selection 2: Yellow tulip bulb

Red tulip bulb = 12

Yellow tulip bulb = 11

Purple tulip bulb = 10

Total tulip bulbs = 33

So,

P(Selection 2: Yellow tulip bulb) = 11/33 = 0.3333

So,

P(First Red& Second Yellow) = 0.3824 X 0.3333 = 0.1275

Case 2: Selection 1: Yellow & Selection 2: Red:

Selection 1: Yellow tulip bulb

Red tulip bulb = 13

Yellow tulip bulb = 11

Purple tulip bulb = 10

Total tulip bulbs = 34

So,

P(Selection 1: Yellow tulip bulb) = 11/34 = 0.3235

Selection 2: Red tulip bulb

Red tulip bulb = 13

Yellow tulip bulb = 10

Purple tulip bulb = 10

Total tulip bulbs = 33

So,

P(Selection 2: Red tulip bulb) = 13/33 = 0.3939

So,

P(First Yellow & Second Red) = 0.3235 X 0.3939 = 0.1274

So,

P(one bulb is Red & the other Yellow) = 0.1275 + 0.1274 = 0.2549

So

Answer is:

0.2549