Question

max is playing a game with his brother. he has a deck of cards with various shapes on the cards. the table shows the number of each shape and the prize his brother will win if he picks that shape. max shuffles the deck and his brother randomly selects a card. \

$$\begin{tabular}{|l|l|l|} \\hline shape & number of cards & prize \\\\ \\hline heart & 10 & sticker \\\\ \\hline diamond & 8 & bouncing ball \\\\ \\hline square & 5 & pencil \\\\ \\hline circle & 2 & rainbow pen \\\\ \\hline \\end{tabular}$$

what is the probability that maxs brother wins a sticker or bouncing ball? explain your answer

Explanation:

Step1: Find total number of cards

First, we need to find the total number of cards. We add up the number of cards for each shape: \(10 + 8 + 5 + 2\).
\(10+8 = 18\), \(18 + 5 = 23\), \(23+2 = 25\). So total number of cards is \(25\).

Step2: Find number of favorable cards

Next, we find the number of cards that give a sticker (Heart) or a bouncing ball (Diamond). The number of Heart cards is \(10\) and Diamond cards is \(8\). So the number of favorable cards is \(10 + 8=18\).

Step3: Calculate probability

Probability is the number of favorable outcomes divided by total number of outcomes. So the probability \(P=\frac{\text{Number of favorable cards}}{\text{Total number of cards}}=\frac{18}{25}\).

Answer:

The probability that Max's brother wins a sticker or bouncing ball is \(\frac{18}{25}\) (or \(0.72\) or \(72\%\)). We first find the total number of cards by adding \(10 + 8+5 + 2 = 25\). Then we find the number of cards that result in a sticker (Heart, \(10\) cards) or a bouncing ball (Diamond, \(8\) cards), so \(10 + 8 = 18\) favorable cards. Probability is favorable over total, so \(\frac{18}{25}\).