A hotel has 2 rooms by the seashore and 4 rooms by the golf course vacant. If you check in, what are the chances you'll get a room by the seashore? 

Solution

• Rooms by the seashore: 2
• Total number of rooms available: 6
• Probability of receiving a room by the seashore: 2/6 = 1/3

Angelita has some marbles in two bags. In one bag she has 3 orange, 3 black and 3 yellow marbles. In the other bag she has 3 orange, 4 black and 5 yellow marbles. If Angelita takes one marble out of each bag, how likely is it that neither one is orange? 

Solution

• Calculate the probability that both bags yielded black or yellow marbles.
• Probability that bag one yielded a black or yellow marble: 6/9
• Probability that bag two yielded a black or yellow marble: 9/12
• Probability that Angelita did not draw an orange marble: 6/9 × 9/12 = 1/2

In the morning Angelita goes fishing at Wide Pond, and in the afternoon at Shallow Pond. The fish in Wide Pond are 1 carp and 2 sunfish, and in Shallow Pond they are 2 carp and 6 sunfish. If Angelita catches one fish in each pond, how likely is it that both are the same kind of fish?

Solution

• Add the probability that both fish are carp and the probability that both are sunfish.
• Probability that the fish from Wide Pond is a carp: 1/3
• Probability that the fish from Wide Pond is a sunfish: 2/3
• Probability that the fish from Shallow Pond is a carp: 2/8
• Probability that the fish from Shallow Pond is a sunfish: 6/8
• Probability that both fish are carp: 1/3 × 2/8 = 1/12
• Probability that both fish are sunfish: 2/3 × 6/8 = 1/2
• Probability that both are carp OR both are sunfish: 1/12 + 1/2 = 7/12

On Monday and Wednesday night, Mrs. Miller went to bed listening to her favorite music CD. The CD contains music from 2 different composers: 4 tracks are Scarlatti and 4 tracks are Debussy. Her stereo is programmed to play the tracks in a random order. How likely is it that on both nights the last track played was Scarlatti?

Solution

• Probability that Monday night the last track was Scarlatti: 4/8
• Probability that Wednesday night the last track was Scarlatti: 4/8
• Probability of finishing with Scarlatti both Monday and Wednesday: 4/8 × 4/8 = 1/4

Alejandro has some candies in his pockets. In his left pocket he has 1 chocolate and 4 lollipops. In his right pocket he has 3 chocolates and 1 lollipop. If Alejandro takes one candy out of each pocket, what is the probability that at least one of the candies is a chocolate?

Solution

• Calculate the probability that neither candy was a chocolate (both were lollipops), and subtract this fraction from 1.
• Probability that he drew a lollipop from his left pocket: 4/5
• Probability that he drew a lollipop from his right pocket: 1/4
• Probability that both candies were lollipops (neither was a chocolate): 4/5 × 1/4 = 1/5
• Probability that at least one candy was a chocolate: 1 - 1/5 = 4/5

Solution 2

• Calculate all cases.
  1. Left pocket chocolate and right pocket chocolate: 1/5 × 3/4 = 3/20
  2. Left pocket chocolate and right pocket lollipop: 1/5 × 1/4 = 1/20
  3. Left pocket lollipop and right pocket chocolate: 4/5 × 3/4 = 12/20
  4. Left pocket lollipop and right pocket lollipop: 4/5 × 1/4 = 4/20
• Cases 1-3 above are successes for drawing a chocolate.
• Probability that at least one candy was a chocolate: 3/20 + 1/20 + 12/20 = 16/20 = 4/5