Question

1. a spinner has 4 equal sections; red, green, blue and orange. ricardo is going to spin the spinner twice. he uses the chart below to help him determine the probability of an event. what is the probability that the spinner will land on a blue section at least once? express your answer as a fraction in simplest form.

Explanation:

Step1: Find the probability of not landing on blue.

The probability of not landing on blue in one - spin is $\frac{3}{4}$ since there are 3 non - blue sections out of 4 total sections.

Step2: Find the probability of not landing on blue in two spins.

Since the spins are independent events, the probability of not landing on blue in two spins is $\frac{3}{4}\times\frac{3}{4}=\frac{9}{16}$ (using the multiplication rule for independent events $P(A\cap B)=P(A)\times P(B)$).

Step3: Find the probability of landing on blue at least once.

The probability of landing on blue at least once is the complement of the probability of not landing on blue at all. So, $P = 1-\frac{9}{16}=\frac{16 - 9}{16}=\frac{7}{16}$.

Answer:

$\frac{7}{16}$