Probability of independent eventsA spinner has 10 equally sized sections, 7 of which are gray and 3 of which are blue. The spinner is spun twice. What is the probability that the first spin landson gray and the second spin lands on blue?Write your answer as a fraction in simplest form.



Answer :

Thouse events are independent, so we can calculate them separately and the final rpobability will be the product of them.

[tex]P(A\, and\, B)=P(A)\cdot P(B)[/tex]

The first event, say A, is of landing on gray. Since 7 out of the 10 are gray, the probability is:

[tex]P(A)=\frac{7}{10}[/tex]

Th second event, B, is of landing on blue. Since 3 out of the 10 are blue, the probability is:

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

So, the probability of both is:

[tex]P(A\, and\, B)=P(A)\cdot P(B)=\frac{7}{10}\cdot\frac{3}{10}=\frac{21}{100}[/tex]