Combined Probability

What is the sample spaces for the combined event below:

Two books are chosen at random from a bookshelf that contains a history book (H), two mathematics books (M) and a geography book (G)

• {(H,M1),(H,M2),(H,G),(M1,M2),(M1,G),(M2,G)}

• (H,M1),(H,M2),(H,G),(M1,H),(M1,M2),(M1,G),(M2,H),(M2,M1),(M2,G),(G,H),(G,M1),(G,M2)

• {(H,M1),(H,M2),(H,G),(M1,H),(M1,M2),(M1,G),(M2,H),(M2,M1),(M2,G),(G,H),(G,M1),(G,M2)}

• (H,M1),(H,M2),(H,G),(M1,M2),(M1,G),(M2,G)

Determine whether the following event is dependent event or independent event:

Vincent and Bajat sit for a Mathematics test in school. Vincent and Bajat pass the Mathematics test.

• INDEPENDENT EVENT

• DEPENDENT EVENT

Box A contains a red card and two yellow cards. Box B contains three red cards and a yellow card. Nelly chooses a card from Box A and Box B respectively. Calculate the probability that Nelly gets two yellow cards.

Box K and Box L contain four cards labelled with the letter "L,I,K,E" and three cards labelled with the numbers "5,6,7" respectively. A card is chosen at random from Box K and Box L respectively. Calculate the probability of getting a vowel and an even number.

A fair dice with four faces is labelled "1,2,3,4". The dice is rolled twice and the numbers that the dice lands on are recorded. By listing all the possible outcomes, calculate the probability of getting two odd numbers.

• 1

A coin is tossed and a dice is rolled simultaneously. By listing the sample of all the possible outcomes of the event, find the probability that a head and an odd number are obtained?

A coin is tossed and a dice is rolled simultaneously. By listing the sample of all the possible outcomes of the event, find the probability that a head or a number greater than 4 are obtained.

Seven cards labelled with the letters "B,A,H,A,G,I,A" are put in a box. A card is chosen at random.

L is the event of getting a vowel

M is the event of getting a consonant

N is the event of getting a letter "B"

Calculate the probability of combined event L or N to occur.

Eight cards labelled with the letters "T,H,U,R,S,D,A,Y" are put in a box. A card is chosen at random from the box. Calculate the probability that the card chosen is labelled with a vowel or letter "R".