EXERCISE:1. The probability that it will rain on a given day is 63%. A child has a 12% chance of falling in dryweather and is three times as likely to fall in wet weather.Draw a tree diagram to represent all outcomes of the above information.What is the probability that a child will not fall on any given day?What is the probability that a child will fall in dry weather?
Question
EXERCISE:1. The probability that it will rain on a given day is 63%. A child has a 12% chance of falling in dryweather and is three times as likely to fall in wet weather.Draw a tree diagram to represent all outcomes of the above information.What is the probability that a child will not fall on any given day?What is the probability that a child will fall in dry weather?
Solution
To solve this problem, we first need to understand the different probabilities given and how they relate to each other.
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The probability of rain on a given day is 63%, so the probability of dry weather is 37% (100% - 63%).
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The probability of the child falling in dry weather is 12%.
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The child is three times as likely to fall in wet weather, so the probability of the child falling in wet weather is 36% (12% * 3).
Now, let's draw a tree diagram:
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Start with two branches, one for rain (63%) and one for no rain (37%).
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From the rain branch, draw two more branches: one for the child falling (36%) and one for the child not falling (64%, which is 100% - 36%).
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From the no rain branch, draw two more branches: one for the child falling (12%) and one for the child not falling (88%, which is 100% - 12%).
Now, we can calculate the probabilities:
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The probability that a child will not fall on any given day is the sum of the probability of not falling in wet weather and the probability of not falling in dry weather.
P(Not Fall) = P(Rain) * P(Not Fall | Rain) + P(No Rain) * P(Not Fall | No Rain)
P(Not Fall) = 0.63 * 0.64 + 0.37 * 0.88 = 0.402 + 0.326 = 0.728 or 72.8%
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The probability that a child will fall in dry weather is simply the probability of no rain times the probability of falling given no rain.
P(Fall | No Rain) = P(No Rain) * P(Fall | No Rain)
P(Fall | No Rain) = 0.37 * 0.12 = 0.0444 or 4.44%
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