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Dancan Nyareru Onchangwa

Dancan N.

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Questions asked

INSTANT ANSWER

7. For a particular machine, the probability that it will break down within a week is \( 0.009 \). The manufacturer has installed 800 machines over a wide area. Calculate the probability that (a) 5 , (b) 9 , (c) less than 5 , (d) more than 4 machines breakdown in a week.

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INSTANT ANSWER

4) A solid metal of ball is falling in along a liquid column and has attained a terminal velocity of \( 6 \mathrm{~m} / \mathrm{s} \). what is viscosity of the liquid if the radius of the metal ball is \( \mathrm{r}=8 \mathrm{~cm} \) and density of \( 8050 \mathrm{~kg} / \mathrm{m}^{3} \). The a density of the liquid is \( 1000 \mathrm{~kg} / \mathrm{m}^{3} \) and \( \mathrm{g}=9.81 \mathrm{~ms}^{-2} \) [3 marks]

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3) Two gas containers with volumes of \( 100 \mathrm{~cm}^{3} \) and \( 1000 \mathrm{~cm}^{3} \) respectively are connected by a tube of negligible volume and contain air at a pressure of \( 1000 \mathrm{mmHg} \). If the temperatures of both vessels are originally \( 0^{\circ} \mathrm{C} \), how much air will pass through the connecting tube when the temperature of the smaller is raised to \( 100^{\circ} \mathrm{C} \) ? Give your answer in \( \mathrm{cm}^{3} \) measures at \( 0^{\circ} \mathrm{C} \) at \( 760 \mathrm{mmHg}[3 \mathrm{marks}] \quad \mid \quad I_{\text {nitial }}=1100 \times 1000 \quad 226863 p+309963 p= \)

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INSTANT ANSWER

8. One-half percent of the population has AIDS. There is a test to detect AIDS. A positive test result is supposed to mean that you have AIDS but the test is not perfect. For people with AIDS, the test misses the diagnosis \( 2 \% \) of the times. And for the people without AIDS, the test incorrectly tells \( 3 \% \) of them that they have AIDS. (9 marks) (a) What is the probability that a person picked at random will test positive? (4 marks) (b) What is the probability that you have AIDS given that your test comes back positive? (4 marks)

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ANSWERED

Kari Hasz verified

Numerade educator

3. Consider three events A, B and C. Show that P(A ? B ? C) = P(A) + P(B) + P(C) ? P(A ? B) ? P(B ? C) ? P(A ? C) + P(A ? B ? C)

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ANSWERED

Robin Corrigan verified

Numerade educator

6. Find the probability of getting a sum of (a) 7 when tossing a pair of dice. (b) at least 4 when tossing a pair of dice.

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ANSWERED

Sanchit Jain verified

Numerade educator

The symmetric difference between two events A and B is the set of all sample points that are in exactly one of the sets and is often denoted A ? B. Note that A ? B = (A ? B) ? (A ? B). Prove that P(A ? B) = P(A) + P(B) ? 2P(A ? B).

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