Carbon tetrachloride or tetrachloromethane (CCl4_4) is a liq…

Carbon tetrachloride or tetrachloromethane (CCl4_4) is a liquid compound that was formerly used as a precursor for refrigerants, as an anti-parasitic agent, or as a component of hard-surface cleaners. However, after the discovery of serious health and environmental dangers associated with CCl4_4 its use is now limited to specialized industrial applications. We learned during the lecture that chlorine atoms naturally occur as a mix of isotopes with relative abundances of: 35^{35}Cl: ≈0.75=75%=3/4\approx 0.75 = 75\% = 3/4 37^{37}Cl: ≈0.25=25%=1/4\approx 0.25 = 25\% = 1/4 What is the probability to find exactly one 37^{37}Cl atoms in a single CCl4_4 molecule?

You perform an experiment that, based on experience from you…

You perform an experiment that, based on experience from your lab mates, should lead to a success in 2 out of 3 cases. You perform the experiment three times in a row and all experiments fail. Assuming that your lab mates are correct, what is the probability of three consecutively failing experiments?