A hat contains 7 scarves, two of which are blue. A bag contains 10 marbles, 3 of which are red. One scarf is randomly selected from the hat and one marble is randomly selected from the bag. Which expression gives the probability of selecting one blue scarf and one red marble?

GIVEN: A hat contains [tex]7[/tex] scarves, two of which are blue. A bag contains [tex]10[/tex] marbles, [tex]3[/tex] of which are red. One scarf is randomly selected from the hat and one marble is randomly selected from the bag.

TO FIND: probability of selecting one blue scarf and one red marble.

SOLUTION:

Let [tex]\text{A}[/tex] be the event getting one blue scarf from hat.

probability getting one blue scarf from hat, [tex]\text{P(A)}=\frac{\text{total blue scarf}}{\text{total scarf in hat}}[/tex]

[tex]\text{P(A)}=\frac{2}{7}[/tex]

Let [tex]\text{B}[/tex] be the event getting one red marble from bag

probability getting one red marble , [tex]\text{P(B)}=\frac{\text{total red marble in bag}}{\text{total marbles in bag}}[/tex]

[tex]\text{P(B)}=\frac{3}{10}[/tex]

As both [tex]\text{A}[/tex] and [tex]\text{B}[/tex] are independent events

Using multiplication rule

[tex]\text{probability getting one blue scarf and red marble}=\text{P(A)}\times\text{P(B)}[/tex]

[tex]=\frac{2}{7}\times\frac{3}{10}[/tex]

[tex]=\frac{1}{35}[/tex]

probability of selecting one blue scarf and one red marble is [tex]\frac{1}{35}[/tex]