# When a British travelling company reduces fares of a particular trip from London to Nottingham. A small taxi can carry four passengers. The time betwe

When a British travelling company reduces fares of a particular trip from London to Nottingham. A small taxi can carry four passengers. The time between calls for tickets is exponentially distributed with a mean of 30 minutes. Assume that each call orders one ticket. What is the probability that the taxi is filled in less than 3 hours from the time of the fare reduction?

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averes8

Given $$\displaystyle\mu={M}{e}{a}{n}={30}$$ minutes
Formula probability exponential distribution: ​​​​​​$$\displaystyle​​​​​​{P}{\left({x}\le{a}\right)}={1}-\frac{{e}^{ -{{a}}}}{\mu}$$

Let us evaluate the formula at x=180 (as 3 hours are 180 minutes): $$\displaystyle{P}{\left({x}\le{180}\right)}={1}-{e}^{ -{{\left(\frac{180}{{30}}\right)}}}={1}-{e}^{ -{{6}}}={1}-{\left(\frac{1}{{c}^{6}}\right)}~{0.9975}={99.75}\%$$