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You can take Bus 65 or Bus 79. You take the first bus that arrives. The probability that Bus 65 arrives first is 75%. There is a 40% chance that Bus 65 picks up passengers along the way. There is a 60% chance that Bus 70 picks up passengers along the way. Your bus picks up passenger. What is the probability that it was Bus 65?

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shubhamchouhanvrVT

The probability that it was Bus 65 will be 66.67%

What is probability?

Probability is defined as the chances of occurence of any random event. Now in the question we will find the probability of the bus 65 to pick up the passengers.

for that we will apply the formula for conditional probability.

[tex]P(X|B)=\dfrac{P(X\cap B)}{P(B)}[/tex]

Here X= Event that you take bus 65

S= event that you take bus 75

B=Bus picked up passengers

[tex]P(X|B)=\dfrac{P(X\cap B)}{P(B)}=\dfrac{P(X)\times P(B|X)}{P(X)(P(B|X)+P(S)(P(B|S)}[/tex]

[tex]P(X|B)= \dfrac{0.75\times 0.4}{(0.74\times 4)+(0.6\times 0.25)}}=\dfrac{0.5}{0.45}=0.667=66.67\%[/tex]

Hence the probability that it was Bus 65 will be 66.67%

To know more about probability follow

https://brainly.com/question/24756209

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