Use the multiplication rule to determine the probability of an intersection of events - High school Statistics & Probabilities Exercises

James throws two unbiased dice.

Let A be the event : "the result of the first die is odd".
Let B be the event : "the result of the second die is 4 or less".

Calculate P\left(A\cap B\right).

P\left(A\cap B\right)=0.4

P\left(A\cap B\right)=\dfrac13

P\left(A\cap B\right)=\dfrac23

P\left(A\cap B\right)=\dfrac56

In a standard 52 card deck, we draw two cards one by one and replace them each time.

Let A be the event : "the first card is a queen".
Let B be the event : "the second card is a heart".

Calculate P\left(A\cap B\right).

P\left(A\cap B\right)=0.1

P\left(A\cap B\right)=\dfrac1{52}

P\left(A\cap B\right)=\dfrac1{13}

P\left(A\cap B\right)=\dfrac16

In a family with three children:

Let A be the event : "the first two children are girls".
Let B be the event : "the third child is a boy".

Calculate P\left(A\cap B\right).

P\left(A\cap B\right)=0.2

P\left(A\cap B\right)=\dfrac{1}{8}

P\left(A\cap B\right)=\dfrac{1}{4}

P\left(A\cap B\right)=\dfrac{1}{6}

A jar contains 7 blue marbles, 4 red marbles, and 9 white marbles. We pick two marble one by one and replace them every time.

Let A be the event : "the first marble is red".
Let B be the event : "the second marble is not white."

Calculate P\left(A\cap B\right).

P\left(A\cap B\right)=0.09

P\left(A\cap B\right)=0.11

P\left(A\cap B\right)=0.15

P\left(A\cap B\right)=0.24

We flip a coin four times:

Let A be the event : "we get exactly two tails on the first tree flips".
Let B be the event : "we get a head on the fourth flip".

Calculate P\left(A\cap B\right).

P\left(A\cap B\right)=0.4

P\left(A\cap B\right)=\dfrac{3}{16}

P\left(A\cap B\right)=\dfrac{2}{9}

P\left(A\cap B\right)=\dfrac5{16}

We roll a fair die four times:

Let A be the event : "the sum of the first two numbers is 9."
Let B be the event :"the sum of the third and fourth number is 3".

Calculate P\left(A\cap B\right).

P\left(A\cap B\right)=\dfrac{1}{36}

P\left(A \cap B\right) =\dfrac{1}{162}

P\left(A\cap B\right)=\dfrac1{72}

P\left(A\cap B\right)=\dfrac1{216}

In a standard 52 card deck, we draw two cards one by one and replace them every time.

Let A be the event : "the first card is an ace".
Let B be the event : "the second card is a face".

Calculate P\left(A\cap B\right).

P\left(A\cap B\right)=0.3

P\left(A\cap B\right)=\dfrac{3}{169}

P\left(A\cap B\right)=\dfrac{3}{52}

P\left(A\cap B\right)=\dfrac9{26}