Question

in an experiment, the probability that the white mouse will be alive for 7 hours is 7/10 and that of a black mouse will be alive for 10 hrs is 9/10. find the probability that at the end of ten hours , a) both the mice will be alive b) only the black mouse will be alive c) only the white mouse will be alive d) atleast one mouse will be alive

Answer 1

Answer on Question #78786 – Math – Statistics and Probability

Question

In an experiment, the probability that the white mouse will be alive for 7 hours is 7/10 and that of a black mouse will be alive for 10 hrs is 9/10. find the probability that at the end of ten hours, a) both the mice will be alive b) only the black mouse will be alive c) only the white mouse will be alive d) at least one mouse will be alive

Solution

a) $P(\text{both alive}) = \frac{7}{10} \cdot \frac{9}{10} = 0.63$

b) $P(\text{only black alive}) = \frac{9}{10} \cdot \left(1 - \frac{7}{10}\right) = 0.27$

c) $P(\text{only white alive}) = \frac{7}{10} \cdot \left(1 - \frac{9}{10}\right) = 0.07$

d) $P(\text{at least one alive}) = 1 - P(\text{both die}) = 1 - \left(1 - \frac{7}{10}\right)\left(1 - \frac{9}{10}\right) = 0.97$

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