Question

there are 10 red, 8 blue, and 4 white buttons in a bag. What is the chance of taking out either a blue or a white button​

Answer 1

Understanding the question :-

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This question, deals with probability. Probability is the prediction of how likely an event is to happen. In hindi, probability is called संभावना.

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In our day to day life, we use probability very frequently. And to make our work easier, mathematicians have derived a formula for probability, and that is :-

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$\qquad \: \star \: \blue{ \underline{ \boxed{ \sf P(E) = \frac{No. \: of \: trials \: of \: that \: particular \: event }{Total~number~of~trials} }}} \: \star$

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Here, P (E) depicts probability of an event. Now, we will use this formula to calculate our answer.

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Given Information :-

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A bag, in which :-

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• Number of red buttons = 10
• Number of blue buttons = 8
• Number of white buttons = 4

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To Find :-

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Probability of taking out :-

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• White button
• Blue button

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Formula Used :-

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$\qquad \: \star \: \purple{ \underline{ \boxed{ \sf P(E) = \frac{No. \: of \: trials \: of \: that \: particular \: event }{Total~number~of~trials} }}} \: \star$

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Solution :-

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First of all, we will calculate the total number of buttons, we get :-

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$\\ \sf \dashrightarrow Total~number~of~buttons = 10 + 8 + 4 \\ \\ \\ \sf \dashrightarrow Total~number~of~buttons = 22 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

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Now, probability for taking out white button :-

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$\\ \sf \dashrightarrow P ( E) = \dfrac{number~of~white \: buttons}{Total~number~of~buttons} \\ \\ \\ \sf \dashrightarrow P ( E) = \cancel \frac{4}{22} = \frac{2}{11} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

Now, probability for taking out blue button :-

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$\\ \sf \dashrightarrow P ( E) = \dfrac{number~of \: blue \: buttons}{Total~number~of~buttons} \\ \\ \\ \sf \dashrightarrow P ( E) = \cancel \frac{8}{22} = \frac{4}{11} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

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$\sf \bull \: Probability ~of~taking~out= \begin{cases} \sf1. ~Blue~button = \dfrac{4}{11} \: \star \\ \\ \\ \sf2. ~White~button = \dfrac{2}{11} \: \star \end{cases}$

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Answer 2

Answer:

6% because

Step-by-step explanation:

10 buttons in all.

1st event: green = 2/10

With replacement, so everything is reset

2nd event: red = 3/10

Combined: 2/10 x 3/10 = 6/100 = 3/50 = 6%