Question

in a packet of stickers there are 6 small stars, 7 big stars, 10 small rockets, and 6 big rockets. manuel is going to choose one of these stickers from the packet at random to put on his artwork. what is the probability that the sticker manuel chooses is small or is a rocket? do not round intermediate computations, and round your answer to the nearest hundredth. (if necessary, consult a list of formulas.)

Explanation:

Step1: Calculate total number of stickers

Total number of stickers \(=6 + 7+10 + 6=29\)

Step2: Calculate number of small stickers

Number of small stickers \(=6 + 10=16\)

Step3: Calculate number of rocket stickers

Number of rocket stickers \(=10 + 6=16\)

Step4: Calculate number of small - and - rocket stickers

Number of small - and - rocket stickers (small rockets) \(=10\)

Step5: Use the formula \(P(A\cup B)=P(A)+P(B)-P(A\cap B)\)

Let \(A\) be the event of choosing a small sticker and \(B\) be the event of choosing a rocket sticker.
\(P(A)=\frac{16}{29}\), \(P(B)=\frac{16}{29}\), \(P(A\cap B)=\frac{10}{29}\)
\(P(A\cup B)=\frac{16 + 16- 10}{29}=\frac{22}{29}\approx0.76\)

Answer:

\(0.76\)