Please Help Probability Problem

Lucas uses only two modes of transport to travel between his home and his school: his bicycle or the bus. If the weather is nice, Lucas uses his bicycle 9 times out of 10. If the weather is poor, he only uses his bicycle 4 times out of 10. Let p be the probability that the weather is nice, on a given day, where Lucas lives. a) Given that the probability that Lucas does not use his bicycle to go to school is 0.33, calculate the value of p to two decimal places b) If Lucas used his bike to go to school, calculate the probability that the weather was nice that day.

Btw: Please keep the answer understandable

#Combinatorics

Easy Math Editor

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Comments

Step 1) Rewrite the given information

   Pn = 0.9, where Pn represent the probability of riding bike on nice weather.
   Pb = 0.4, where Pp represent the probability of riding bike on bad / poor weather.
   p represent the probability of the weather is nice.

Step 2) Draw the diagram

                                              Taking bike (Probability = Pn = 0.9)
   Weather nice (Probability = p) -----------<
                                              Not taking bike (Probability = 1 - Pn = 1 - 0.9 = 0.1)

                                              Taking bike (Probability = Pb = 0.4)
   Weather bad / poor (Probability = 1 - p) --<
                                              Not taking bike (Probability = 1 - Pb = 1 - 0.4 = 0.6)

Step 3) Solve for p

   The probability of Lucas doesn't use his bike is 0.33 or equal to probability of not using bike on nice weather and 
   probability of not using bike on bad / poor weather.
   p (1 - Pn) + (1 - p) (1 - Pb) 
   = p (0.1) + (1 - p) (0.6)
   = 0.1 p + 0.6 - 0.6 p
   = -0.5 p + 0.6

   -0.5 p + 0.6 = 0.33
   -0.5 p = -0.27
   p = 0.54

Quest Keeper - 6 months, 3 weeks ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$